Preheat broiler. In a medium bowl combine crabmeat, mayonnaise, sour cream, green onion, dill, and lemon juice; set aside. In a small bowl combine butter and cayenne pepper.
Generously spread outsides of English muffin halves with butter mixture. Place four of the muffin halves, buttered sides down, on a baking sheet. Top with cheese. Broil 4 to 5 inches from the heat 1 to 2 minutes or until cheese starts to melt.
Spoon crab mixture onto cheese-topped muffin halves, spreading to edges. Top with the remaining muffin halves, buttered sides up.
Heat a large griddle or skillet over medium heat. Add sandwiches; cook 6 minutes or until muffins are golden brown, turning once. Cut each sandwich into four portions.