You see few service dogs in Lima so I bet if there are rules, people would be pretty oblivious to them. Probably a lot depends on their personal criteria, and whether you really seem to need the dog as an aid or not. In any case, I´d suggest some kind of vest for the dog in order to identify it as an aid dog. Nothing like a uniform to get some respect! But these are just opinions...
I know of one agency that trains dogs, so if anyone knows the answer to your question, they do. Why not try to get in touch with them? https://www.facebook.com/bocalanperu.taa
All the best,