Preheat the oven to 375 degrees . Heat an outdoor grill or cast iron skillet over medium-high.
Arrange the bacon on a broiler pan or parchment-lined baking sheet. Bake until crisp, 15 to 18 minutes, then chop.
Season the steak with Worcestershire and salt and pepper; drizzle with EVOO. Cook to desired doneness, 4 to 5 minutes per side for medium-rare. Let rest 5 minutes.
In a large bowl, whisk the lemon juice, garlic, mustard and vinegar. While whisking, slowly stream in 3 tbsp. EVOO; season. Toss the greens and onions with the dressing; divide among plates.
Slice the steak against the grain. Top greens with the steak, bacon and cheese.