My mother is from a Serbian family that makes wonderful leg of lamb. Her secret--which sounds strange--is to add a whole green pepper to the roasting pan. Something about the pepper suffuses the lamb with a delicate, hard-to-explain but delicious flavor. She also inserts slivers of garlic into the meat (as do I) and roasts until it is very tender.

I find that a lot of the gamey flavor you're talking about resides in the fatty tissue of the lamb. Try to find a relatively lean cut first off. Otherwise, trim the fat a bit before cooking. You can also pair the lamb with something acidic--a tomato sauce, for instance. That should cut down on it some.
Interestingly, a lot of sheep's milk cheeses have something of a strange flavor as well, due largely to the lanolin that sheeps produce to keep their pelt water-resistant. If you've ever touched an unwashed sheepskin, you know what I mean.

Here's a good website for making lamb less gamey:
http://www.livestrong.com/article/555171-how-to-remove-the-game-smell-when-cooking-lamb-chops/

I'm not a big fan of lamb for that exact reason. On a recent trip to Paris, I finally tasted a lamb that was utterly delicious. It was a boneless leg of lamb, roasted with herb paste. After several attempts, and conferring with various cookbooks, I think I have come close to the lamb in Paris!

I make a "paste" from minced garlic, parsley, rosemary, anchovies, dijon, S&P, lemon zest. Add enough olive oil so that you can easily spread in the nooks and crannies of the boneless leg of lamb. Re-tie the lamb and bake as usual. Lamb medium rare, has the least gamey taste to me.

I personally think New Zealand lamb tastes "gamey" and will not buy it. American Lamb, however , well it's the best!! (No gamey taste that I can discern)