You could use any one of three cuts for this dish: a leg, boned and butterflied; a rack (in which case it should be roasted rather than grilled): or, my preferred option, fillet of best end (long cut). This is a good choice when the lamb has grown up a bit and is no longer quite such a baby (what they mysteriously call 'hoggit' in the North of England). The cut consists of the 'eye', which runs from the neck (the scrag end) through to the loin,. Ask for the bones and trimmings if you want to make lamb stock, otherwise don’t worry about throwing them away. Much better to do so immediately than bag and freeze to discard at a later date.
The couscous flavoured with mint, garlic, lemon juice and oil is a very Middle-Eastern salad, and a perfect accompaniment to the lamb.