Remove the lamb chops from the refrigerator and massage the chopped thyme, 1/2 teaspoon of the salt, and pepper into the meat. Set the lamb chops aside at room temperature for 5 minutes.
Melt 2 tablespoons of the butter in a 12-inch skillet over medium-high heat. Add the lamb chops and cook until a rich, brown crust forms on the bottom, 4 to 6 minutes (if you're using thicker lamb chops, this could take up to 10 minutes).
Flip the lamb chops and continue to cook until an instant-read thermometer inserted into the thickest part of the meat registers 145°F, 4 to 6 minutes more.
Transfer the lamb chops to a plate and cover with aluminum foil. Discard all but 2 tablespoons of the rendered fat.
Reduce the heat to medium. Add the shallot, garlic, and thyme sprig to the pan and cook until shallot softens and begins to brown, about 1 minute.
Deglaze with the wine or broth and lemon juice, scraping any browned bits from the bottom of the pan.
Cook until reduced by half, 1 to 2 minutes. Stir in the lemon zest, remaining ¼ teaspoon salt, and 2 tablespoons butter.
Cook until the butter melts and the sauce thickens slightly, about 1 minute. Taste and season with more salt and pepper if needed.
Pour the sauce over the lamb chops and serve immediately.