I had a vegetarian dog that lived to 18 and very healthy. She was born with hip displaysia so she eventually couldn't go to the bathroom very well because she couldn't stand or squat to poop without struggling a lot. It was only toward the end that it was bad, but she didn't need anything other than routine vet check ups and shots her whole life.
Our other vegetarian dog was 13, and she died of brain tumors. She was a very healthy and active Husky. She was active till the day she had to be put down. Both of them were larger dogs. One was 45 lbs and the other was about 55 lbs. We had both of them since they were puppies.
All of our dogs are vegetarian or vegan depending on what type of dog food we could get. We often used Nature's Recipe, Natural Balance, and we did do a homemade vegan diet too. It was a complete diet with supplements that we had to add to the recipe and it was formulated according to AAFCO standards. I liked that one a lot, but I got too busy to make the food. It was called Vege-Dog (Vege-Pet), and I know it's still for sale online. There is a new one called V-dog, but I haven't tried it yet.
V-dogfood — Welcome