Does anyone know where you can buy goat in downtown Manhattan, or Brooklyn?
Also - is there a part of a lamb that is similar to skirt steak?
Yes, there is a vendor at Union Square that always has very good goat, but I don't remember the name either. They are at the north end of the market., easy to find I love skirt steak and I love lamb so I can understand the desire for something that combines both, but I don't think there is such a thing as lamb skirt steak. Lambs are much smaller than cows and are built somewhat differently, so I don't think anything comparable exists.
Check Patches of Stars and Lynnhaven at the Union Square Greenmarket. They're more well known for their goat cheese but they often have goat meat for sale.
This NYT lists some retail stores that have it as well:
Union Square Greenmarket
Broadway and E 17th St, New York, NY 10003