In a small bowl, combine mayonnaise, ketchup, and mustard.

If made ahead, cover and refrigerate until the next day.

Arrange meat on cooking grate.

Place lid on grill.

Cook, turning once halfway through cooking time, until meat is browned and hot throughout (2 to 4 minutes).

Slice sausages diagonally 3/4 inch thick.

On a platter, arrange lettuce, cheese, eggs, pickles, celery, tomatoes, and onion in 7 separate rows.

Serve with mayonnaise mixture.