How to Make It
In a baking dish, whisk the olive oil with the lemon juice, garlic, rosemary and thyme. Add the lamb and turn to coat. Cover and refrigerate for 8 hours or overnight, turning occasionally. Bring the lamb to room temperature before grilling.
In a medium bowl, whisk the yogurt with the lemon zest, lemon juice, thyme and rosemary. Season the sauce with salt and pepper.
In a saucepan, combine the vinegar with the sugar, orange juice and 1 cup of water; bring to a boil over moderately high heat. Add the eggplant and cook for 2 minutes. Off the heat, let the eggplant cool completely in the liquid, about 45 minutes. Drain well.
Light a grill or preheat a grill pan. Remove the lamb from the marinade and season with salt and pepper. Grill over high heat, turning once, until charred outside and medium-rare within, about 6 minutes total. Transfer the chops to plates and let rest for 5 minutes.
In a bowl, toss the drained pickled eggplant with the cucumber, olives and arugula. Season the salad with salt and pepper. Serve the lamb with the salad, passing the yogurt sauce at the table.