Scrub live clams and mussels under cold running water. Using your fingers, pull out the beards from the mussels that are visible between the shells.
In a large pot combine cold water and 1/3 cup of salt. Add clams and mussels; soak for 15 minutes. Drain and rinse.
Place clams and mussels in the bottom of a foil pan. Top with chorizo (Optional), potatoes, and corn. Place lobster tails on top. Cover pan with foil; seal tightly.
Place foil pan on the rack of an uncovered grill directly over medium coals. Grill for 20 to 30 minutes.
Transfer clam mixture to a serving platter, reserving cooking liquid. Serve with vegetables aside.