Perhaps I'm being pedantic, to the point, most Indian food is vegetarian, not vegan. They love their milk, cheese, and honey.
"Ghee is widely used in South Indian cuisine for tempering curries, in preparation of rice dishes and sweets. South Indians have a habit of adding ghee to their rice before eating it with pickles and curries. South Indians are one of the biggest consumers of ghee."
With a bit of effort, you can eliminate animal products from most vegetarian Indian food. It will taste different, but not too much.
Source: I'm Indian.