Heat oven to 400° F. In a large resealable plastic bag, combine 1/4 cup of the oil, the fennel seeds, cumin, 1 teaspoon of the salt, and the pepper. Add the lamb chops and refrigerate for at least 30 minutes and up to 8 hours.
Before cooking, let the chops stand at room temperature for 10 minutes. Heat a large skillet over medium-high heat. Scrape the fennel seeds off the chops. Add 4 of the chops to the skillet. Cook until golden, about 2 minutes per side. Transfer to a baking sheet. Repeat with the remaining chops. Roast until the chops are the desired doneness, about 8 minutes for medium-rare.
Meanwhile, wipe out the skillet, place over medium heat, and add the remaining oil. Add the carrots and chickpeas and cook until heated through, about 2 minutes. Add the lemon juice, mint, and the remaining salt and toss. Divide the chops and chickpeas among individual plates.
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