Heat a large cast iron skillet over medium-high heat. Add the olive oil and butter to melt.
Using the salt, pepper, and thyme, season the catfish on both sides. Carefully place the fillets into the skillet.
Let them cook for 2-3 minutes then flip with a large spatula.
Squeeze the juice from half a lemon onto the second side of the fish. Cook for another 2-3 minutes.
Remove the fish from the skillet with a spatula and place onto serving plates. Squeeze lemon juice over top and garnish with chopped parsley