Here's how I got Laravel Airlock working with NuxtJS and the native Authentication module: https://serversideup.net/using-laravel-airlock-with-nuxtjs/

AirlockNuxt

Testing Laravel Airlock with Nuxt

Build Setup

# install dependencies
$ npm run install

# serve with hot reload at localhost:3000
$ npm run dev

# build for production and launch server
$ npm run build
$ npm run start

# generate static project
$ npm run generate

For detailed explanation on how things work, check out Nuxt.js docs.