Well it's a known issue that laravel doesn't really work on shared hosting. You need ssh access which you don't have most of the time on shared hosting. You also need services like composer and newer PHP versions.
So, like I said before in another thread, you are better off setting up a VPS for your Laravel projects and host them yourself. If you really have no idea how to handle the server stuff you should take a look at https://forge.laravel.com For only $10 a month you get a complete system for deployment and spinning up new websites.
Tell your boss that you need to keep your WordPress and Laravel sites separated from each other.