Laravel / Lumen and shared hosting are not exactly best friends. For Laravel / Lumen apps, you need to be able to have full SSH access and complete folder structure control, also known as your own server.
Last time I tried to add a Laravel project on shared hosting, it ended up being way too limited and I was able to add the project files in the public_html folder which ruined the URL paths.
Some shared hostings might allow full SSH access and folder access, but you have to check that in the features they offer.