Prepare the grill for direct cooking over medium-low heat (150º to 180ºC) and preheat a perforated grill pan on one side of the grill.
Combine the rub ingredients. Brush both sides of the lamb chops with oil and season evenly with the rub. Allow the chops to stand at room temperature for 15 to 30 minutes before grilling.
Brush the eggplant and onion slices all over with oil, and then grill in a single layer on the grill pan over direct medium-low heat, with the lid closed, until browned and tender, 10 to 12 minutes, turning occasionally. Remove the vegetables and the pan from the grill and increase the temperature of the grill to medium-high heat (200° to 230°C).
Put the tomato pieces into a large bowl. While still warm, cut the eggplant and onion into bite-sized pieces and add to the bowl. Their warmth will gently heat the tomatoes. Add the mint, lemon juice, 2 tablespoons oil, the coriander, salt, and pepper and toss to combine. Cover to keep warm while grilling the lamb chops.
Grill the lamb chops over direct medium-high heat, with the lid closed, until cooked to your desired doneness, 7 to 9 minutes for medium rare, turning once. Remove from the grill and serve with the warm vegetable salad.
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