Hadn't thought about it in-depth, but it's obvious that Luke Tryon is unemployed. He's had jobs throughout his life, but he can't keep one for too long (he has ADHD and gets bored easily, or makes mistakes)
So, yeah, he's lived with his parents (now parent) rent-free for some time--momma's boy type. Now that his mom's gone, he's getting pressured to take on some form of employment, of which you'll see hopefully in the near future.
I will say, however, he is currently enjoying running the chicken rescue/farm, though he is not officially the manager/owner (it's technically not an official business, just something that Teresa Tryon did on the side)
*Kinda making this up as I go along...Maybe Luke will create a webcomic on a clucky friar and sell it for a living XD