Combine mayonnaise and mustard; set aside. Cut each carrot slice into three triangles; set aside.
For each lion, place half of a hamburger bun, cut side up, on an ungreased baking sheet (three lions per sheet). Spread with a small amount of the mayonnaise mixture. Top with a slice of Swiss cheese. Add two olives for eyes, a carrot triangle for nose and two pimientos for mouth. Position the top half of a hot dog bun, cut side up, below head for body. Spread with mayonnaise mixture. Top with turkey and American cheese, cutting to fit the bun.
For the tail, slice 1/2 in. from one end of the hot dog bun bottom. Cut remaining portion into four 2-1/4-in. strips for legs. Position the legs and tail with cut side up; spread with mayonnaise mixture.
Cut one slice of American cheese into strips to fit over legs and tail. Place over the mayonnaise mixture, tucking under cheese of the body.
Broil 6 in. from the heat until cheese is slightly melted and the lion holds its shape, about 2 minutes. Sprinkle shredded cheese on the end of the tail and around head. Broil 30 seconds longer or until cheese is melted.
Transfer to a serving plate. Add potato sticks for whiskers. If desired, add lettuce under legs for grass.
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