As with humans, an increased thrist and urinating can be a sign of diabetes, but a vet will be able to test for diabetes at consultation... (it was thought that my old spaniel might have this, alongside his infection, vet did the test proved negative)
I would suggest with your neighbours it obvious that your dog and your neighbour enjoy there little interaction (I know I had a neighbour who would share a cream cake with our dog on a saturday morning over the fence enjoyed by both) what I would do is buy some acceptable treats take them around, explain now the dog is an old you need to consider her weight and diet... But you be more than happy if they change to giving her/him the supplied treats setting the ration per day/treat, never know your luck the next lot of treats they might buy themselves
Flippent comments at times of stress....
Mind you it's not all about money, but by having the treatment carried out what are you going to put the dog through and what is the quaility of life is going to be for the dog durning and after the treatment?
I have in the past paid a lot to have my pet treated at the vets, but based on that the treatment required, once sorted the animal then could continual a pain free happy life, I have also refused treatment due to our cocker spaniel age 16 and felt that it was unfair to put an animal through an operation followed by chemo (if he survived the op in the first place)...