Quick touches are the key to good steak sandwiches: In 15 minutes, the beef absorbs the flavors of the marinade, and sliced onions become a sweet-tart component.
Pierce steak all over with a fork. Place in a shallow dish, and rub with Worcestershire; season with salt and pepper. Let stand at least 15 minutes. In a small bowl, combine onion, 4 tablespoons vinegar, and sugar; season with salt and pepper. Let stand at least 15 minutes.
In a large skillet, heat 1 tablespoon oil over medium-high. Cook steak 6 minutes. Turn, and cover; reduce heat to medium. Cook until medium-rare, 6 to 8 minutes (if steak is browning too quickly, reduce heat to medium-low). Transfer to a plate; let rest 10 minutes. Thinly slice against the grain.
While steak rests, stir together 2 tablespoons vinegar and 1 tablespoon oil in a serving bowl; season with salt and pepper. Add lettuce, and toss.
Spread 4 slices of bread with Dijon; top with steak and onion. Close sandwiches; serve with salad.
Steak doesn't have to be a splurge when you pick good-value cuts like top round or skirt.