If you are allergic to lamb and mutton, you may have to take extreme caution while in Turkey. Lamb/mutton is the “national meat” and is used in all sorts of dishes: grills/kebaps (of course), but also as stock for soups, stews and sauces, and in stuffed vegetables and some savory pastries.
Even if you were to eat vegetarian dishes (which is possible), restaurant staff may use utensils “contaminated” with lamb to serve it.
Food allergies and their potential seriousness (and fatal consqeuences) are even more poorly understood in Turkey than in North America and Europe.
I would venture to say that allergies are hardly recognized at all, so even if you were to tell restaurant staff:
Kuzu etine çok ciddi alerjim var, ölebilirim!
(koo-ZOO eht-tee-neh CHOHK jee-DEE ahl-lehr-ZHEEM vahr, EARL-eh-bee-LEE-reem, “I have a very serious allergy to lamb/mutton meat, I could die!”)
…I don’t think they would really understand what it meant in real-life terms. Some might even think you were joking.
I hesitate to recommend that anyone with lamb allergy stay clear of most restaurant food, but you may have to do that, at least most of the time, and eat yoghurt, fruit, bread, salads and snacks.