Sometimes I get headaches from eating lamb but I love lamb. Why is this?

It's a food allergy! One to one connection with eating lamb and headaches is like eating strawberries and getting itchy swollen lips and tongue, even when you love strawberries. Shell fish, especially shrimp is another perfect example of food allergy. Perhaps the most common food allergy is peanuts specifically, and nuts generally.
Lamb headache. Its hard to make any correlation but is worth exploring two pathway to your answer. Is the lamb cooked with monosodium glutamate to enhance flavoring. Msg has been correlated with the onset of headaches (baad-hansen et al 2010). The other possibility your brain is already pre conditioned to get a headache when you eat lamb making anxiety more prominent. So ask about the seasoning.