Split lobster shells lengthwise, cutting through hard upper shells and underneath shells with kitchen shears. Remove lobster meat through split shells. Discard shells.
Snap off tough ends of asparagus. Remove scales from stalks with a knife or vegetable peeler, if desired.
Combine juice and 1/2 teaspoon curry powder. Place asparagus and lobster tails on rack of a broiler pan coated with cooking spray. Brush one half of juice mixture over lobster and asparagus. Broil 5 1/2 inches from heat (with electric oven door partially opened) 12 minutes, basting often with remaining juice mixture. Remove from oven; cut lobster meat into 1/2-inch-thick slices.
Combine remaining 1/2 teaspoon curry powder, sour cream, chutney, and cilantro, stirring well. Arrange asparagus spears and lobster slices on individual serving plates. Serve with chutney sauce.