I haven't done lamb chops or rack of lamb, but my favorite way to cook lamb is as Souvlaki.
You need skewers and you start with a boneless leg of lamb, usually around 5 lbs. It is a bit of work to break the leg down into nice small cubes, an inch or 3/4, and discard the fat. Once you have it on the skewers, salt it with a half teaspoon per pound of meat and let it sit for a while, probably at least an hour would be great. Then in your food processor turn the following into a paste:
half a yellow onion
a bunch of parsley, fresh
a bunch of oregano, fresh
1-2 teaspoons of black pepper
2 tablespoons olive oil
Once you're ready to cook, dump the paste on your skewered meat and manuver them around to coat the meat evenly. I usually grill them over high, direct heat, I suspect they could be broiled in the oven as well.
Serve with some lemon wedges on flatbread, tzatziki sauce, hummus, cherry tomatoes, maybe some good olives and strong red wine, perhaps zinfandel. I also like some sriracha sauce on mine.