Heat oil in a large cast iron pan over medium-high heat. Sprinkle fish all over with salt and pepper.
When oil shimmers, add fish, and cook until flesh is opaque, about 3 to 5 minutes. Turn fish over and cook on second side until just opaque in center, about 3 to 5 minutes more.
Transfer fish to plates; serve with a few slices of lemon, and a few spoonfuls of green sauce. Pass additional sauce on the side.