Fellow lamb lover here, there's a lot of it on property:
Animal Kingdom Lodge: The lamb shank at Sanaa is phenomenal. The lamb chops at Jiko are maybe, maybe, the best meal I've ever had.
The lamb shawarma at Tangerine Cafe is without a doubt the best quick service meal on property, IMO.
Lamb chops at The Wave and Kona Cafe were both excellent.
I haven't had it yet but at Epcot's Flower and Garden there is a lamb chop at The Berry Basket.