Place steaks on a platter and sprinkle with half the dry mustard; pat the steaks with the flat part of a fork to spread the mustard evenly over the meat.
Sprinkle the steaks with half the Worcestershire sauce, then squeeze half the lime over them; pat with the fork.
Season the steaks generously with salt and pepper.
Turn the steaks over and spread with the remaining mustard, Worcestershire sauce, and lime juice, and more salt and pepper, patting with the fork.
Let the steaks marinate for 15-20 minutes while you preheat the grill.
When ready to cook, oil the grill grate.
Place the steaks on the hot grate and grill, turning with tongs, until cooked to taste, 4-6 minutes per side for medium rare; do not rotate steaks here, if you do, you will jar off the mustard mixture.
Transfer the steaks to a platter and let stand for 3 minutes.
Thinly slice the steaks on the diagonal, as you would London broil.
Let the slices marinate in the meat juices for a minute or two, then serve immediately.