Combine 1 tablespoon olive oil, garlic, half the lemon zest and juice, 1/4 teaspoon salt and a few grinds of pepper in a quart-size resealable plastic bag. Crush the thyme sprigs in your hands and toss them in as well. Add the lamb chops and seal the bag. Squeeze the bag and move it around to coat the chops evenly with the marinade. Let sit at room temperature for 30 minutes.
Preheat a grill for indirect and direct cooking over medium-high heat. For gas grills (with 3 or more burners), turn all the burners to medium-high heat; after about 15 minutes turn off one of the middle burners. For charcoal grills, bank one chimney starter-full of lit and ashed-over charcoal briquettes to one side of the grill. Set up a drip pan on the other side to avoid flare-ups. (Be sure to consult the grill manufacturer's guide for best results.)
Stir together the pomegranate seeds, almonds, mint, honey, the remaining 2 tablespoons olive oil and remaining lemon zest and juice, a pinch of salt and a grind of black pepper in a small bowl. Reserve.
Remove the lamb chops from the bag and pat dry. Season all over with salt and pepper. Place the lamb chops medallion-side down on the hot side of the grill and cook to develop dark grill marks, about 4 minutes. Flip the lamb chops and cook for another 4 minutes. Turn the chops fat-cap side down to start rendering the fat, 1 minute. Flip the chops bone-side down and move them to the indirect side of the grill. Cover and cook until an instant-read thermometer inserted in the middle of the chops reads 125 degrees F for medium-rare, 6 to 8 minutes.
Remove the chops and let rest 5 minutes before serving. Spoon some pomegranate-mint pesto over each chop.
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