In a wide bowl, mix olive oil, lemon juice, and mustard.
Trim stalks from fennel. Rinse feathery green leaves and chop enough to measure 1/4 cup; discard remaining leaves and stalks. Trim and discard root end, any bruised areas, and coarse fibers from fennel head; rinse head, thinly slice, and mix with dressing in bowl. Add chopped fennel greens, lettuce, and arugula to bowl.
Lift with salad fork and spoon to mix with dressing. Season to taste with salt and pepper.