This repo shows how you can get sqlite3 installed for using with Ruby.
It uses heroku-buildpacks-multi so that it can run heroku-buildpack-apt and heroku buildpack-ruby at the same time. The dependencies are listed in Aptfile and Gemfile.
To create a Heroku app using heroku-buildpack-multi:
$ heroku create --buildpack https://github.com/ddollar/heroku-buildpack-multi
Or in an existing app:
$ heroku buildpacks:set https://github.com/ddollar/heroku-buildpack-multi.git