Put morels in a bowl and add 2 cups boiling water.
Trim and discard most of the surface fat from lamb.
Place an 11- or 12-inch ovenproof nonstick frying pan over medium-high heat. When pan is hot, put lamb rack, fat side down, in pan and cook until brown, 3 to 4 minutes; tip rack back and forth as needed to color evenly. Remove pan from heat (to reduce spattering) and add 2 tablespoons balsamic vinegar and 2 tablespoons madeira. Return to heat and shake pan until most of the liquid evaporates. Remove form heat again and put lamb, bones down, in a 9- by 13-inch pan. Set frying pan aside.
With your hand gently squeeze the morels in water to release grit. Then lift out the mushrooms and squeeze dry. Holding morels under cool running water, again gently massage and squeeze them to release any grit that remains.
Put morels in frying pan. Pouring carefully, without disturbing grit in bowl, measure 1 cup soaking water and add to pan. Discard remaining water. Add shallots, remaining vinegar and madeira, and butter to frying pan. Cover and place on high heat until boiling, then uncover, and boil gently until liquid is reduced by about a third, about 7 minutes.
Place one oven rack in the lowest postion and another in the center of a 450º oven. Set frying pan with shallot mixture on lowest rack and bake until liquid is thick and bubbling, 18 to 22 minutes, shaking occasionally. Keep warm if ready before lamb.
Meanwhile, insert a meat thermometer into center of narrow end of lamb. Five minutes after the shallots have gone into the oven, put lamb on middle rack and roast until thermometer registers 135º for medium-rare, 12 to 15 minutes (large end will be rare; cook about 5 minutes longer for medium to medium-rare). Remove lamb and let stand at least 5 minutes.
Place lamb on a platter and add shallot mixture. Accompany with watercrss. Cut meat apart between ribs. Season to taste with salt and pepper.