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.
Tip: Lamb loin chops are relatively large and tender cuts of meat. Be sure to ask for them by name or you may end up with rib chops, which are smaller and pricier.
To Freeze: Transfer the large resealable bag of uncooked lamb chops to the freezer or, if desired, freeze the chops in individual bags for single servings. Store for up to 3 months.
To Reheat: Thaw overnight in the refrigerator. Cook according to the recipe.