Add oil to a cast-iron skillet. Heat over medium-high heat until oil begins to bubble.
Season filets of tilefish with salt and pepper to taste. Place filets into the pan with the side that used to have skin facing up; they should not touch each other. Sear for two to three minutes.
Flip the fish carefully and place 2 lemon slices on each filet.
Add smashed garlic cloves, thyme sprigs, and two and butter to the pan. As the butter melts and the thyme and garlic start to sizzle, baste the filets with the mixture. Basting continuously, cook this second side for two to three minutes, or until the fish reaches your desired doneness.
Remove the fish with a slotted spatula, leaving the thyme and garlic behind. Serve with your favorite sous vide or roasted fresh vegetables.