Fill a lobster pot or other large pot two-thirds full with water. Add potatoes, onion, garlic, and salt. Cover, and bring to a boil.
Uncover, reduce heat to medium, and cook until potatoes begin to soften, 8 to 10 minutes. Add lobsters headfirst. Cover, and cook until shells are bright red, 5 to 6 minutes. Add corn, and cook for 3 minutes more.
Remove potatoes, lobsters, and corn from water; discard onion and garlic. Using kitchen shears, clip tips of lobster claws, and let drain. Serve potatoes, lobsters, and corn with butter.