You indeed can inject vape lite into BLC, but you will not be protected from screen shares. Also, do not log into a badlion protected server if you do inject vape lite into it, as you will get banned.
Adding on to what @Abstrax said, Vape Lite isn’t officially supported for Badlion Client. This means that some modules will not work like they’re supposed to, and there will be a lot of bugs. (i.e Misplace is glitchy/non-functional)