Cool! I'm a Vegetarian too!
We have chickens that we only use for eggs, of course, and as company; and trust me, most chickens are great company! Ours are very friendly and are like part of the family.
My dad isn't a Vegetarian, but he knows how much we love the chickens, and he does too.
We haven't had to think about what to do with a chicken if she doesn't keep laying eggs; But if one of them stops, we just keep them. Call me crazy, but I believe that chickens should be treated like humans; not literally, but when it comes to egg production, if a hen wants to stop, shouldn't she be able to?
I mean, if you had an older daughter/son who gave you free food every day, and then suddenly stopped without a reason, would you just say, "Oh well. Lets just cull and eat him/her".
So what we do is if a hen stops laying, we don't really care; she will lay when she wants to lay. No big deal. We have enough eggs anyway. But that's just what we do. We have our chickens for 2 reason; friends and eggs. If they aren't laying, then we can have them as friends. If they are mean and ugly and aren't laying, then we usually rehome them, not eat them It works fine for us.
good luck and happy veggie/non-meat eating!