Preheat oven to 400˚F.
For the croutons, place EVOO in a skillet over medium heat and melt in butter, then add garlic, add bread, and toss to combine and coat evenly. Season croutons with pepper and sprinkle with the cheese. Transfer the croutons to a baking sheet and bake until deeply golden and fragrant, 15-20 minutes. Cool to handle. (You'll have more than you need. Store in tin or wrap in foil for up to 2 weeks.)
For the Caesar dressing, place all ingredients in food processor bowl. Pulse to combine, then turn machine on and stream in the EVOO. Taste to adjust seasoning.
For the steak, preheat a cast iron skillet or griddle over medium-high heat. Season room temp meat with salt and pepper, add a little olive oil to pan and cook steaks about 7-8 minutes for medium rare, turning occasionally; add cut lemon to pan to caramelize it. Douse steaks with lemon. Let the meat rest to settle juices, then slice against the grain.
For each frico egg, heat a 6-inch nonstick skillet over medium heat, add about ½ cup cheese. When cheese bubbles and melts, add egg, cover pan and cook egg to soft, medium or well. Let egg set a minute or 2 to serve.
For the salad, dress the lettuce and the croutons. Top with frico egg, carefully sliding it from skillet with thin spatula and placing it on salad. Serve the steak alongside, off to the edge of the salad.