Can i lose weight on a gluten free vegan diet?

Absolutely: Greasy animal fats are the best-tasting stuff on the planet and if you eliminate them, you'll eat less. Being gluten-free is a huge help to folks with celiac disease / dermatitis herpetiformis so it has turned into a "fad" diet for everybody else -- this has no scientific basis. Why not do yourself a huge favor and go wild for fitness like when you were a teen? Feel great, make friends.

You can, but: Is this necessary for you? A vegan diet restricts protein choices, and gluten-free limits grains and flours plus many other surprising foods (even soy sauce contains gluten!) many people are sensitive to gluten even if they don't have celiac disease. A gluten-free diet may be especially healthy for people with mood and cognitive disorders -- or with metabolic syndrome, etc.