Trim fat from steak. Score steak by making shallow diagonal cuts at 1-inch intervals in a diamond pattern. Repeat on other side. Cut steak in half lengthwise. Place a portion of steak between 2 pieces of plastic wrap. Working from the center to the edges, pound lightly with the flat side of a meat mallet into a 10x6-inch rectangle. Remove plastic wrap. Sprinkle with 1/4 teaspoon of the lemon-pepper seasoning and 1/8 teaspoon of the salt. Arrange 4 bacon slices lengthwise on steak. Repeat with the remaining portion of steak.
Preheat indoor electric grill. For filling, in a medium bowl combine spinach, bread crumbs, thyme, and the remaining lemon-pepper seasoning. Spread half of the filling over each portion of steak. Starting from a short side, roll up each portion into a spiral. Secure with wooden toothpicks at 1-inch intervals, starting 1/2 inch from one end. Cutting between the toothpicks, slice each portion into six 1-inch pinwheels. On each of six 6-inch skewers, thread 2 pinwheels. Remove toothpicks.
Place pinwheels on the grill rack. If using a covered grill, close lid. Grill until steak is desired doneness. (For a covered grill, allow 6 to 7 minutes for medium (160 degrees F). For an uncovered grill, allow 12 to 14 minutes for medium (160 degrees F), turning once halfway through grilling.) To serve, remove pinwheels from skewers. Makes 6 servings.