In large bowl, mix chilles, lobster meat, spinach, Swiss and Cheddar cheeses. Place tortillas flat and spread lobster mixture over, leaving a border. Fold each tortilla in half.
Heat griddle to 325° F. Pour 2 tablespoons butter over and spread evenly. Fry quesadillas, turning until golden brown on both sides and adding butter as necessary. Cut each quesadilla into 3 wedges and serve.