Heat the oil and butter in a large cast iron skillet.
Place the salmon skin-side-up in the skillet and cook until it's just about cooked through (you still want it to be tender throughout, so be careful not to cook it too long-- or at too high of heat). Flip the filets over onto the skin and cook for 2 to 3 more minutes.
Remove from the pan, squeeze with lemon, add salt and pepper, and that's it!