The typical North American way to cook lamb is to put big chunks of it to a BBQ. I don't really do that.
Instead I like to cut lamb or mutton into small cubes, sear them in a pan and then roast them some more in an over so that they are crispy on the outside but still tender on the inside.
Of couse I like things a bit spicier than what most North Americans like (and no sugar on the meat). So I typically buy a nice chunk of lamb and I cut it into cubes. I trim off most of the fat and any odd chewy pieces and cook those with onions, garlic and hot peppers, tomatoes, and lots spices into a curry which is then used to season the end product.
The cubes are then seared in a pan and then I roast them in the oven. If the juices come out and some more fat is rendered during the process that goes into the curry.
At the end the dish is plated on a bed of Basmati rice, then the lamb cubes with lots of curry sauce on top.