Katie, not sure what the laws are where you live, but here where I live it's not appropriate for a nurse/doctor to date a psych patient they are helping and providing therapy to.

He may have offered to have lunch with you just in a friendship way too. Instead of entertaining more than that, it's a good idea to ask him about his intentions so you don't create intentions that are not based in reality. Also, my concern is also that you may very well in your psychological challenge be taken advantage of too, and that's something you don't deserve to experience.