Generously sprinkle the steak with salt and pepper and let sit at room temperature for 5 minutes. Cover the onion with cold water in a small bowl and let sit until ready to use then drain (this will take some of the sharpness out of the onion).
Heat 1/2 tablespoon oil in a medium nonstick skillet over medium-high and cook the steak, until browned on both sides and medium-rare, 3 to 4 minutes per side. Transfer to a cutting board and let rest 10 minutes. Cut into thin slices against the grain.
Meanwhile, wipe out the skillet and heat 1/2 tablespoon oil over medium heat. Crack in the eggs and cook, undisturbed, until the whites are set but the yolks are still runny, 3 to 4 minutes. Season with salt and pepper.
Toss the romaine with the lemon juice, remaining 2 tablespoons oil and season with salt and pepper. Divide salad between 2 plates and top each with half of steak and 1 egg. Top with onion and chili rings.
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