Most of the restaurants will do a lamb shank if you order it in advance.
I remember on our Wedding Anniversary we asked at George's for a traditional Turkish meal to be cooked for the next day. We had a lamb dish that was lovely. Savas told us it was a meal his Mother cooked for special occasions.
The restaurants in Calis cater for the British visitors because they are asked for Full English, Sunday Roasts, Steak Dinners, chips, etc., So it's not surprising they supply what there are asked for.
It is seems now the Brits are realising what is most popular and what we want the most is Turkish Food in Turkey. The shining example of this is the Mozaik Bahce which is always No.1 on T.A. and people come to it from all the resorts around Fethiye to eat they lovely food and why it's so recommended on this Forum.
Time some resourceful Turk opened a Turkish Restaurant in Calis and remembered to keep the standards high and the food always good.