Many years ago, the kitchen I worked at would get a whole lamb carcass and from that we would butcher it for the different night's specials. I learned much at this place.
I have not worked at a restaurant that has served lamb in the last decade it seems, and that was at a high end Italian kitchen that had rack of lamb chops called Agnello Scottadito (Burning fingers as the idea was they could be picked up).
That said, when I was at the Mohegan Sun, there is a place called Big Bubba's BBQ. I won't say that it is southern authentic, but they did have a leg of Kentucky lamb with mustard BBQ sauce.
For those who are curious here is the link. http://www.bigbubbasbbq.com/
As you can see, they charge casino prices and not roadfood cheap for their meals. It was pretty good just by virtue that it was on the menu to begin with.
I see that there is a side thread about buying lamb. I posted recently that searching for lamb breast (ribs) is a worthwhile endeavor. I have not seen them at a normal market. I have found them at a Latino market nearby and they are a great buy and very flavorful. They lend themselves to a variety of sauces. I make a sauce of mint jelly and dijon mustard....yummy.
At these same markets, I see that goat is available. There are Jamaican restaurants that feature it too. I think that I will try it soon just to see what that is all about.