Press paper towel onto steak to dry. Spray with olive oil and sprinkle Lil Texas Spice Rub all over steak. Flip steak over and repeat. Once grill is hot (about 15 minutes) place steak on the hottest part of the grill and cook 7-10 minutes on each side. Grill until you have good grill marks and the steak is medium rare to medium (about 140 degrees F).
Transfer steak to cutting board and let rest, tented with foil, about 10 minutes. Holding thin slicing knife at 45-degree angle to meat, slice very thinly. Prepare bread by slicing in half lengthwise and spreading with steak sandwich sauce. Add lettuce, tomato and onion. Layer slices of steak.
Lil Texas Spice Rub
Combine ingredients in a small bowl. Set aside until ready to use.
Steak Sandwich Sauce
Combine ingredients in a small bowl. Set aside until ready to use.