Combine all the ingredients for the salsa verde in a bowl and season with salt and pepper. Set aside.
Wash the inside and outside of the mullet under cold running water and pat dry with kitchen paper. Cut 2–3 deep slashes along the width of both sides of the mullet, then brush the fish all over with the oil. Season with salt and pepper. Insert a lemon slice into each slash, then tuck a couple of slices inside each fish.
Lay the mullet on a nonstick baking sheet and cook under a preheated very high grill, about 10 cm (4 inches) from the heat source, for about 5 minutes on each side until cooked through and lightly charred. Serve immediately with the salsa verde.