Heat the grill to high. Scrub the grill rack with a grill brush. Use grilling tongs to dip a wad of paper towels in some vegetable oil, and use the oil-dipped paper towels to wipe down the grill rack.
Place the chops in a nonreactive baking dish in a single layer. Sprinkle the lemon juice over the chops, drizzle over the olive oil, and turn the chops to coat both sides with the juice and oil. Sprinkle both sides of the chops with salt and pepper. Let sit at room temperature for 15 minutes while the grill heats.
Grill the chops for about 4 minutes on each side for medium rare, less if you like your chops pinker, more if you like them more well done (see lamb chops grilling chart above). Once the lamb chops are on the grill, baste them with any remaining marinade left in the pan.
Remove from the grill, let sit for two minutes, and serve hot with the Mint Basil Pesto if desired.
Notes
Cook the rib lamb chops to your liking. Remember, thought that the temperature will rise as they rest off the grill. Aim for an internal temperature of 140 F for rare, between 155 F and 160 F for medium, and between 165 F and 170 F for well-done chops.