1. Rinse clams under cold running water; place in a large bowl. Cover with cold water; add black pepper. Let stand 30 minutes; drain and rinse. (This helps clean the clams of any grit.)
2. Add water to a large stockpot to a depth of 2 inches; bring to a boil. Add potatoes and corn; steam, covered, 5 minutes. Add lobsters headfirst, and add clams; steam, covered, 8 to 10 minutes. Discard any unopened clam shells.
3. Combine butter and lemon juice in a small saucepan; cook over medium-low heat until butter melts.
4. Divide lobster, clams, corn, and potatoes among 4 large plates. Ladle broth from bottom of stockpot into a bowl for dipping clams. Serve with melted lemon-butter.