Treats that are safe: Watermelon, cheerios, apple(cut up and peeled), carrots, zuccini, most veggies except onion
He can't have things like bully stix or anything that has animal protein...
Also, I know of a dog that lived to be 17 yrs old and had MVD, so depending on the severity, they can live a fairly normal life

As far as foods, protein on a
dry matter basis needs to be under 18% if your baby was having any symptoms of liver shunt before the surgery.
There are other foods that your baby can eat...Royal Canin Hepatic LS 14 is another that your baby can have. And after a few months, if your baby is symptom free, you may choose to switch him to a vegetarian diet by Avoderm or Natural Balance or something like that as long as it's vegetarian and under 18%.
Also, the lactulose is extremely important...The amount needs to be based on the stool consistency. Stool must be soft,
not firm...Difficult to pick up, but not diarrhea.
Also, you should give your baby supplements like milk thistle and sam-e (also known as denosyl)...These help with liver function...They help protect the liver from further damage and help to repair the already damaged parts...
Sam-E should be given on an empty stomach and food can be given an hour after taking it.
This is just my opinion and I base it on our personal experiences, research that I have done, and experiences from others who have dealt with this.