16 unpeeled garlic cloves plus 1 tbsp. finely chopped garlic 2 tbsp. Break off and discard stem from 1 artichoke. Bend back outer leaves until they snap off close to base and remove several more layers of leaves until pale inner leaves are reached. Cut artichoke into quarters and cut away choke and spiky purple-tipped leaves.
Rub artichoke quarters all over with a remaining lemon quarter and drop it in the bowl of water.
Prepare other 3 artichokes in the same manner, using other lemon quarter if necessary. In a saucepan of boiling salted water, blanch artichokes 3 minutes and with a slotted spoon transfer to a bowl. In boiling salted water blanch Jerusalem artichoke 5 minutes, and drain. Roast vegetables in middle of oven 20 minutes. While skillet is heating, season lamb racks with salt and pepper.