Sri Lankans do not eat out much like people in Southeast Asia! So, there are is a few choices when it comes to the restaurant selection, particularly those in small towns. That said, you should not have the problem of finding a vegan meal. Even in the small towns, you will likely eat at the place you stay, so they can tailor the meal to your request.
However, I did some research and found the following website, which I think would be helpful: