Season fish on both sides with salt. Heat a large nonstick skillet over high. Swirl in 2 teaspoons oil and heat until shimmering. Add fish, flesh-side down, and cook until bottom is golden brown, 3 to 4 minutes. Flip and continue cooking until just opaque throughout, about 2 minutes more. Transfer to a platter.
Meanwhile, whisk together lemon zest and juice, oregano, and remaining 3 tablespoons plus 1 teaspoon oil; season with pepper.
Pour lemon mixture over fish while still hot. Serve warm or at room temperature.