Lamb.....or goat on Long Island
Giunta's Meat Farms (a few stores in Suffolk) is a good start. Any supermarket that serves Latin-American customers (Best Yet, C-Town, Bravo) will probably have goat. ALSO there's a live poultry market in Holbrook, Bello, that also sells sheep and goats (they slaughter them there). Also any halal butcher--there's a good one at Nazar in N. Babylon.
Having said that, any good butcher should have lamb shoulder.