How do I talk to a restaurant about assisting vegans?

[TJRightHere]

I live in India and there is this vegetarian (lacto vegetarian) restaurant near my place. It's kind of popular and they have many vegan choices. But while looking at the menu it's very time consuming and not at all relaxing to hunt for dairy-free dishes. Many of the dishes I order may even contain dairy and I might not even know about it. Also if I tell them I want dishes without any milk products they might not take it seriously and there might be little bit milk products in everything. If they create a dairy free menu then they will realize that the customer seriously wants a dairy free dish. I want to ask the restaurant manager to create a separate menu where they list all their vegan/dairy free dishes from the original menu to make it easier on vegans. Any tips on how can I talk to the manager and make an impact on him so as he really ends up doing it? I was thinking of talking to him from a health perspective because he probably doesn't care about animals. Like telling him I have diabetes and that I am not supposed to consume any dairy products like butter, cream, ghee and that I am also lactose intolerant so I can ask him to cater to his customers that have health and digestive problems. Maybe I can tell him I'll get extremely sick if I consume too much dairy?

[brimstoneSalad]

You could tell him that, yes. Or also tell him that you'll eat there more often. And that you'll help put his restaurant on websites like happy cow that help people find vegan friendly restaurants.

If I knew a vegetarian restaurant had a vegan menu and wasn't confusing, I'd be more likely to go there while traveling. Indian restaurants are always a pain because of the dairy.
I'll choose a vegan place first, but in some areas that's not an option so I choose a vegetarian one and try to make do.