You will need to point your document root to the public folder. PHP 5.5 is required along with MySQL.
To set up the database, you will need to run the following commands in the root directory:
php artisan migrate:install
php artisan migrate:refresh --seed
This will use the migrations in database/migrations and the data contained within the various seeders at database/seeds to both build and populate the database.
Regular tasks will be dealt with by lumen, set this cron to run every minute to allow the app to delegate any jobs.
* * * * * php /path/to/artisan schedule:run >> /dev/null 2>&1