Preheat oven to 450 degrees. On a rimmed baking sheet, toss potatoes with 2 teaspoons oil; season with salt and pepper. Roast until golden brown and tender, 20 minutes. Meanwhile, in a large heavy skillet, heat 1 teaspoon oil over high. Pat steak dry; season steak with salt and pepper and cook until browned and medium-rare, 3 to 5 minutes per side (reduce heat if skillet begins to scorch). Transfer to a cutting board; let rest 5 minutes, then thinly slice against the grain.
In a large bowl, combine romaine and arugula. Add potatoes, lemon juice, and 2 tablespoons oil and toss to combine. Top salad with steak and Parmesan and serve with lemon wedges.