Combine garlic, paprika, 2 tablespoons lemon juice and oil in a large, shallow ceramic dish. Season both sides lamb with salt and pepper. Score lamb skin (this allows marinade to penetrate). Place lamb in marinade and turn to coat. Cover and refrigerate for 3 hours. Remove from fridge 30 minutes before cooking.
Make green olive mayonnaise: Meanwhile, combine mayonnaise, olive, paprika and 1 tablespoon lemon juice in a bowl. Season with salt and pepper. Mix well. Cover and refrigerate until ready to serve.
Spray a cold barbecue plate or grill with oil. Preheat on high heat. Reduce heat to medium-high. Barbecue lamb, skin side down, for 10 minutes. Turn and cook for 5 minutes. Reduce heat to medium-low. Cover lamb with barbecue hood (see tip). Barbecue for a further 15 minutes for medium or until cooked to your liking. Remove from heat. Cover loosely with foil. Set aside in a warm place for 10 minutes to rest. Slice lamb thinly across the grain.
Serve lamb with green olive mayonnaise and jacket potatoes.
Tip: If you don’t have a barbecue with a hood, turn a large roasting pan or foil turkey roaster upside down and use as a hood over lamb.