Special equipment: 6 metal or wooden skewers (if wooden, soaked in water for 30 minutes)
Add the lamb to a large gallon-size resealable plastic bag.
Mix the olive oil, mint, white wine vinegar, garlic, salt, and pepper together in a measuring cup.
Pour the marinade over the lamb, seal the top, and toss the lamb in the marinade, making sure it's completely coated. Place in the refrigerator to marinate for at least 1 hour or up to overnight.
Meanwhile, to make the mint sauce: Add the mint, basil, capers, red pepper flakes, olive oil, white wine vinegar, salt, and pepper to a food processor. Pulse until smooth. Turn off and taste for seasoning, adding more salt and pepper, if needed. Remove to a bowl and refrigerate until serving.
Preheat a grill to medium-high heat. With a clean tea towel, lightly oil the grill grates.
Remove the lamb from the marinade, let excess drip off, and thread onto skewers.
Season the lamb with salt and pepper. Grill for 8 minutes total for medium-rare, turning to cook all sides. Serve on a platter drizzled with sauce.