I am wondering if there is the same (or equivalent) for Lumen? I am using for one of our projects and just want to make sure I don't miss anything in deployment.
Possibly Lumen, by design, does not need these features as it's blazing fast out of the box.
Laravel Lumen doesn't support most of the artisans commands you get with Laravel. The idea of Lumen is to stay as small as possible. Only really useful for an API that handles a lot of data.
So you can't cache the config and so on during deployments. You are able to clear the cache using php artisan cache:clear. You should definitely call this during your deployment.