Lumen does support custom configuration files, but they need to be enabled first.
You need to add calls to $app->configure('file.php') in your bootstrap/app.php. A cleaner method might be to make a config.php to contain the configure calls and then include that file from bootstrap/app.php.
If you want to use .env values directly, you can also uncomment Dotenv::load(__DIR__.'/../'); at the top of bootstrap/app.php. That will allow getenv('name') to work.