Preheat the oven to 220°C. Put the racks of lamb in a roasting pan, season well and cook in the oven until done to taste (20 minutes for rare, 25 minutes for medium rare, 30 minutes for well done). Remove from the oven and allow to cool, then refrigerate for at least 4 hours. Cut the racks into cutlets and place on one or two wire trays set over a baking dish.
Stir the mint and vinegar into the aspic and chill until it starts to become syrupy. Quickly spoon it over each lamb cutlet, coating them evenly. (If the aspic starts to set, stand the container in a bowl of hot water, stir quickly until melted, then continue.) Chill the cutlets until the aspic is set, then repeat the coating process until all the aspic is used.
For a buffet, arrange the cutlets on a bed of lettuce on one large tray, with a cutlet frill on each bone. Refrigerate until serving time.
For a picnic, put the lettuce on serving dishes or in containers that will fit into your cool boxes. Put a cutlet frill on each bone and arrange the cutlets on the lettuce. Cover the dishes with plastic wrap, making sure the plastic does not touch the cutlets and spoil their perfect glazed appearance.