Pat the lamb dry with paper towels and season both sides with salt and the 1/4 cup za'atar. Set aside on a baking sheet.
Cut one lemon half into 5 thin slices and set aside.
Heat 2 tablespoons of the neutral oil in a large cast-iron or other heavy-bottomed skillet over high heat until almost smoking. Add the scallions, lemon slices and lemon halves cut-side down. Season with salt and cook, flipping the scallions and lemon slices, until charred and softened, 4 to 5 minutes. Set aside to cool. Wipe out the skillet with a paper towel.
Add the remaining 4 tablespoons neutral oil to the same skillet and heat over high heat until shimmering, about 1 minute. Add the lamb chops and cook until browned, 3 to 4 minutes per side. Turn the chops so the fatty edge of each makes direct contact with the hot skillet and cook until seared, about 1 minute longer. Set the lamb aside to rest.
Meanwhile, remove the seeds from the lemon slices and finely chop the lemon slices. Transfer to a medium bowl. Finely chop the scallions and add to the bowl along with the remaining 1 tablespoon za'atar, the juice of 1 charred lemon half, the yogurt and 1/2 cup olive oil. Season with salt and pepper and stir together. Taste and adjust the seasoning.
Spoon the charred lemon yogurt onto a platter, top with the lamb chops, drizzle with olive oil and garnish with mint, if using. Serve with the remaining charred lemon halves and enjoy.
Remove the lamb from the refrigerator 15 to 20 minutes before cooking to take the chill off.