Combine lime juice, soy sauce, garlic, ginger, sugar, salt and pepper in a shallow bowl or platter and marinate the steak for at least 30 minutes (if the marinating time is longer than an hour, refrigerate).
Near the end of the marinating time, start a charcoal or wood fire or preheat a gas grill or broiler; make it very hot.2.
Remove the meat from the marinade and dry well with paper towels.
Grill or broil the steak about 4 inches from the heat source for 3 to 4 minutes per side, or until nicely browned.
Move the meat to a cooler part of the grill (or lower the broiling rack) and cook for another 2 minutes per side.
Check for doneness by touch, with a thin-bladed knife, or, preferably, with an instant-read thermometer (125 degrees is about right for rare to medium-rare).3.
Let rest for 5 minutes before cutting into thin slices, across the grain, using a sharp carving knife.
4. Separate lettuce leaves and arrange on a platter.
Combine mayonnaise and sriracha and place in serving bowl.
5. Serve sliced steak, lettuce leaves, kimchi and sriracha dipping sauce on a platter and let guests assemble their own rolls.