Where can you buy used lawn tractor engines?

Try mower dealers who may have trade-ins or repair shops which may have replaced engine, but then it is probably going to need fixing. As you don't say in your question where you are it is difficult to offer other helpful suggestions.

You can try googleing "used lawn tractor engines near (your zip code),, or try eBay.

Many areas also have mower junkyards that may have serviceable engines mounted to "trashed" frames.