diff --git a/libs/parallelism/algorithms/include/hpx/parallel/algorithms/lexicographical_compare.hpp b/libs/parallelism/algorithms/include/hpx/parallel/algorithms/lexicographical_compare.hpp
index cce3698424bd..83f07254950b 100644
--- a/libs/parallelism/algorithms/include/hpx/parallel/algorithms/lexicographical_compare.hpp
+++ b/libs/parallelism/algorithms/include/hpx/parallel/algorithms/lexicographical_compare.hpp
@@ -250,7 +250,8 @@ namespace hpx { namespace parallel { inline namespace v1 {
                               std::size_t part_count,
                               std::size_t base_idx) mutable -> void {
                     util::loop_idx_n(base_idx, it, part_count, tok,
-                        [&pred, &tok](reference t, std::size_t i) -> void {
+                        [&pred, &tok, &proj1, &proj2](
+                            reference t, std::size_t i) -> void {
                             using hpx::get;
                             using hpx::util::invoke;
                             if (invoke(pred, invoke(proj1, get<0>(t)),
diff --git a/libs/parallelism/algorithms/tests/unit/container_algorithms/CMakeLists.txt b/libs/parallelism/algorithms/tests/unit/container_algorithms/CMakeLists.txt
index 93b5807d86cd..3f13ab5bf70f 100644
--- a/libs/parallelism/algorithms/tests/unit/container_algorithms/CMakeLists.txt
+++ b/libs/parallelism/algorithms/tests/unit/container_algorithms/CMakeLists.txt
@@ -53,6 +53,7 @@ set(tests
     is_partitioned_projection_range
     is_sorted_range
     is_sorted_until_range
+    lexicographical_compare_range
     make_heap_range
     max_element_range
     merge_range
diff --git a/libs/parallelism/algorithms/tests/unit/container_algorithms/lexicographical_compare_range.cpp b/libs/parallelism/algorithms/tests/unit/container_algorithms/lexicographical_compare_range.cpp
new file mode 100644
index 000000000000..e1594075f3d5
--- /dev/null
+++ b/libs/parallelism/algorithms/tests/unit/container_algorithms/lexicographical_compare_range.cpp
@@ -0,0 +1,281 @@
+//  Copyright (c) 2018 Christopher Ogle
+//  Copyright (c) 2020 Hartmut Kaiser
+//
+//  SPDX-License-Identifier: BSL-1.0
+//  Distributed under the Boost Software License, Version 1.0. (See accompanying
+//  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include <hpx/iterator_support/tests/iter_sent.hpp>
+#include <hpx/local/init.hpp>
+#include <hpx/modules/testing.hpp>
+#include <hpx/parallel/container_algorithms/lexicographical_compare.hpp>
+
+#include <cstddef>
+#include <iostream>
+#include <iterator>
+#include <numeric>
+#include <string>
+#include <vector>
+#include <algorithm>
+
+#include "test_utils.hpp"
+
+////////////////////////////////////////////////////////////////////////////
+unsigned int seed;
+std::mt19937 gen;
+std::uniform_int_distribution<> dis(0, 25);
+
+void test_fill_sent()
+{
+    std::vector<char> c1(10);
+    std::generate(
+        std::begin(c1), std::end(c1), []() { return 'a' + dis(gen); });
+
+    std::vector<char> c2(10);
+    std::generate(
+        std::begin(c2), std::end(c2), []() { return 'a' + dis(gen); });
+
+    bool actual_result1 = std::lexicographical_compare(
+        std::begin(c1), std::begin(c1) + 5, std::begin(c2), std::begin(c2) + 5);
+    bool result1 = hpx::ranges::lexicographical_compare(std::begin(c1),
+        sentinel<char>{*(std::begin(c1) + 5)}, std::begin(c2),
+        sentinel<char>{*(std::begin(c2) + 5)});
+
+    bool actual_result2 = std::lexicographical_compare(
+        std::begin(c2), std::begin(c2) + 5, std::begin(c1), std::begin(c1) + 5);
+    bool result2 = hpx::ranges::lexicographical_compare(std::begin(c2),
+        sentinel<char>{*(std::begin(c2) + 5)}, std::begin(c1),
+        sentinel<char>{*(std::begin(c1) + 5)});
+
+    bool actual_result3 = std::lexicographical_compare(
+        std::begin(c1), std::begin(c1) + 5, std::begin(c1), std::begin(c1) + 5);
+    bool result3 = hpx::ranges::lexicographical_compare(std::begin(c1),
+        sentinel<char>{*(std::begin(c1) + 5)}, std::begin(c1),
+        sentinel<char>{*(std::begin(c1) + 5)});
+
+    HPX_TEST_EQ(actual_result1, result1);
+    HPX_TEST_EQ(actual_result2, result2);
+    HPX_TEST_EQ(actual_result3, result3);
+
+    // check corner cases
+    std::vector<char> c3 = {1, 1, 1, 1, 3, 2, 2, 8};
+    std::vector<char> c4 = {1, 1, 1, 1, 3, 5, 5, 8};
+    auto result4 = hpx::ranges::lexicographical_compare(
+        std::begin(c3), sentinel<char>{3}, std::begin(c4), sentinel<char>{3});
+    auto result5 = hpx::ranges::lexicographical_compare(
+        std::begin(c3), sentinel<char>{8}, std::begin(c4), sentinel<char>{8});
+
+    HPX_TEST_EQ(false, result4);
+    HPX_TEST_EQ(true, result5);
+}
+
+template <typename ExPolicy>
+void test_fill_sent(ExPolicy policy)
+{
+    static_assert(hpx::is_execution_policy<ExPolicy>::value,
+        "hpx::is_execution_policy<ExPolicy>::value");
+
+    std::vector<char> c1(10);
+    std::generate(
+        std::begin(c1), std::end(c1), []() { return 'a' + dis(gen); });
+
+    std::vector<char> c2(10);
+    std::generate(
+        std::begin(c2), std::end(c2), []() { return 'a' + dis(gen); });
+
+    bool actual_result1 = std::lexicographical_compare(
+        std::begin(c1), std::begin(c1) + 5, std::begin(c2), std::begin(c2) + 5);
+    bool result1 = hpx::ranges::lexicographical_compare(policy, std::begin(c1),
+        sentinel<char>{*(std::begin(c1) + 5)}, std::begin(c2),
+        sentinel<char>{*(std::begin(c2) + 5)});
+
+    bool actual_result2 = std::lexicographical_compare(
+        std::begin(c2), std::begin(c2) + 5, std::begin(c1), std::begin(c1) + 5);
+    bool result2 = hpx::ranges::lexicographical_compare(policy, std::begin(c2),
+        sentinel<char>{*(std::begin(c2) + 5)}, std::begin(c1),
+        sentinel<char>{*(std::begin(c1) + 5)});
+
+    bool actual_result3 = std::lexicographical_compare(
+        std::begin(c1), std::begin(c1) + 5, std::begin(c1), std::begin(c1) + 5);
+    bool result3 = hpx::ranges::lexicographical_compare(policy, std::begin(c1),
+        sentinel<char>{*(std::begin(c1) + 5)}, std::begin(c1),
+        sentinel<char>{*(std::begin(c1) + 5)});
+
+    HPX_TEST_EQ(actual_result1, result1);
+    HPX_TEST_EQ(actual_result2, result2);
+    HPX_TEST_EQ(actual_result3, result3);
+
+    // check corner cases
+    std::vector<char> c3 = {1, 1, 1, 1, 3, 2, 2, 8};
+    std::vector<char> c4 = {1, 1, 1, 1, 3, 5, 5, 8};
+    auto result4 = hpx::ranges::lexicographical_compare(policy, std::begin(c3),
+        sentinel<char>{3}, std::begin(c4), sentinel<char>{3});
+    auto result5 = hpx::ranges::lexicographical_compare(policy, std::begin(c3),
+        sentinel<char>{8}, std::begin(c4), sentinel<char>{8});
+
+    HPX_TEST_EQ(false, result4);
+    HPX_TEST_EQ(true, result5);
+}
+
+template <typename IteratorTag>
+void test_lexicographical_compare(IteratorTag)
+{
+    std::vector<char> c1(10);
+    std::generate(std::begin(c1), std::end(c1),
+        []() { return 'a' + dis(gen); });
+
+    std::vector<char> c2(10);
+    std::generate(
+        std::begin(c2), std::end(c2), []() { return 'a' + dis(gen); });
+
+    bool actual_result1 = std::lexicographical_compare(
+        std::begin(c1), std::end(c1), std::begin(c2), std::end(c2));
+    bool result1 = hpx::ranges::lexicographical_compare(c1, c2);
+
+    bool actual_result2 = std::lexicographical_compare(
+        std::begin(c1), std::end(c1), std::begin(c2), std::end(c2));
+    bool result2 = hpx::ranges::lexicographical_compare(c1, c2);
+
+    bool actual_result3 = std::lexicographical_compare(
+        std::begin(c1), std::end(c1), std::begin(c2), std::end(c2));
+    bool result3 = hpx::ranges::lexicographical_compare(c1, c2);
+
+    HPX_TEST_EQ(actual_result1, result1);
+    HPX_TEST_EQ(actual_result2, result2);
+    HPX_TEST_EQ(actual_result3, result3);
+}
+
+template <typename ExPolicy, typename IteratorTag>
+void test_lexicographical_compare(ExPolicy policy, IteratorTag)
+{
+    static_assert(hpx::is_execution_policy<ExPolicy>::value,
+        "hpx::is_execution_policy<ExPolicy>::value");
+
+    std::vector<char> c1(10);
+    std::generate(
+        std::begin(c1), std::end(c1), []() { return 'a' + dis(gen); });
+
+    std::vector<char> c2(10);
+    std::generate(
+        std::begin(c2), std::end(c2), []() { return 'a' + dis(gen); });
+
+    bool actual_result1 = std::lexicographical_compare(
+        std::begin(c1), std::end(c1), std::begin(c2), std::end(c2));
+    bool result1 = hpx::ranges::lexicographical_compare(policy, c1, c2);
+
+    bool actual_result2 = std::lexicographical_compare(
+        std::begin(c1), std::end(c1), std::begin(c2), std::end(c2));
+    bool result2 = hpx::ranges::lexicographical_compare(policy, c1, c2);
+
+    bool actual_result3 = std::lexicographical_compare(
+        std::begin(c1), std::end(c1), std::begin(c2), std::end(c2));
+    bool result3 = hpx::ranges::lexicographical_compare(policy, c1, c2);
+
+    HPX_TEST_EQ(actual_result1, result1);
+    HPX_TEST_EQ(actual_result2, result2);
+    HPX_TEST_EQ(actual_result3, result3);
+}
+
+template <typename ExPolicy, typename IteratorTag>
+void test_fill_async(ExPolicy policy, IteratorTag)
+{
+    static_assert(hpx::is_execution_policy<ExPolicy>::value,
+        "hpx::is_execution_policy<ExPolicy>::value");
+
+    std::vector<char> c1(10);
+    std::generate(
+        std::begin(c1), std::end(c1), []() { return 'a' + dis(gen); });
+
+    std::vector<char> c2(10);
+    std::generate(
+        std::begin(c2), std::end(c2), []() { return 'a' + dis(gen); });
+
+    bool actual_result1 = std::lexicographical_compare(
+        std::begin(c1), std::end(c1), std::begin(c2), std::end(c2));
+    hpx::future<bool> result1 =
+        hpx::ranges::lexicographical_compare(policy, c1, c2);
+
+    bool actual_result2 = std::lexicographical_compare(
+        std::begin(c1), std::end(c1), std::begin(c2), std::end(c2));
+    hpx::future<bool> result2 =
+        hpx::ranges::lexicographical_compare(policy, c1, c2);
+
+    bool actual_result3 = std::lexicographical_compare(
+        std::begin(c1), std::end(c1), std::begin(c2), std::end(c2));
+    hpx::future<bool> result3 =
+        hpx::ranges::lexicographical_compare(policy, c1, c2);
+
+    result1.wait();
+    result2.wait();
+    result3.wait();
+
+    HPX_TEST_EQ(actual_result1, result1.get());
+    HPX_TEST_EQ(actual_result2, result2.get());
+    HPX_TEST_EQ(actual_result3, result3.get());
+}
+
+template <typename IteratorTag>
+void test_lexicographical_compare()
+{
+    using namespace hpx::execution;
+
+    test_lexicographical_compare(IteratorTag());
+    test_lexicographical_compare(seq, IteratorTag());
+    test_lexicographical_compare(par, IteratorTag());
+    test_lexicographical_compare(par_unseq, IteratorTag());
+
+    test_fill_async(seq(task), IteratorTag());
+    test_fill_async(par(task), IteratorTag());
+
+    test_fill_sent();
+    test_fill_sent(seq);
+    test_fill_sent(par);
+    test_fill_sent(par_unseq);
+}
+
+void lexicographical_compare_test()
+{
+    test_lexicographical_compare<std::random_access_iterator_tag>();
+    test_lexicographical_compare<std::forward_iterator_tag>();
+}
+
+////////////////////////////////////////////////////////////////////////////
+int hpx_main(hpx::program_options::variables_map& vm)
+{
+    unsigned int seed1 = (unsigned int) std::time(nullptr);
+    if (vm.count("seed"))
+        seed1 = vm["seed"].as<unsigned int>();
+
+    std::cout << "using seed: " << seed1 << std::endl;
+    std::srand(seed1);
+
+    seed = seed1;
+    gen = std::mt19937(seed);
+
+    lexicographical_compare_test();
+    return hpx::local::finalize();
+}
+
+int main(int argc, char* argv[])
+{
+    // add command line option which controls the random number generator seed
+    using namespace hpx::program_options;
+    options_description desc_commandline(
+        "Usage: " HPX_APPLICATION_STRING " [options]");
+
+    desc_commandline.add_options()("seed,s", value<unsigned int>(),
+        "the random number generator seed to use for this run");
+
+    // By default this test should run on all available cores
+    std::vector<std::string> const cfg = {"hpx.os_threads=all"};
+
+    // Initialize and run HPX
+    hpx::local::init_params init_args;
+    init_args.desc_cmdline = desc_commandline;
+    init_args.cfg = cfg;
+
+    HPX_TEST_EQ_MSG(hpx::local::init(hpx_main, argc, argv, init_args), 0,
+        "HPX main exited with non-zero status");
+
+    return hpx::util::report_errors();
+}