I'm not too familiar with places downtown or in the close in suburbs since I don't venture in there too often, but I've had lamb dishes at Clyde's in the past. Like all of their food it was delicious. Their menus change day to day and vary between restaurants though; right now the online menu for Gallery Place does not list lamb but the Georgetown one does. The 1789 restaurant on Clyde's website also seems to have lamb on their menu, but I've never been there.

Gadsby's Tavern (http://www.gadsbystavernrestaurant.com/) in Old Town Alexandria is another one to consider. That's all I can think of offhand.