In a large resealable plastic bag, coat the lamb with the ⅓ cup of aioli. Season with salt and pepper. Refrigerate for at least 2 hours and up to overnight. Let sit at room temperature for 30 minutes before cooking.
If using wooden skewers, submerge them in water in a large baking dish. Let soak for at least 1 hour; drain. Thread the lamb onto 6 to 8 skewers, giving your meat a little space so it browns evenly.
Preheat a grill to medium-high (350-400°F), indirect cooking (for a charcoal grill, bank coals on one side of grill; for a gas grill, leave one or two burners off) and oil the grate. Grill the skewers over direct heat, turning every minute or so, until browned and beginning to char in spots, about 4 minutes. Move to the cooler side of the grill and continue to grill until the lamb is medium-rare within, about 4 minutes more.
Meanwhile, grill the red onion, turning occasionally, until tender and nicely charred, about 10minutes.Transfer the lamb skewers and red onion to a platter and cover with foil. Grill the naan until beginning to char and is soft and pliable, 2 to 3 minutes.
Arrange the skewers, naan, and red onion on a large platter. Drizzle the lamb with more Coconut Curry Aioli.
Add sliced tomato, Persian cucumber, herbs, and lemon wedges to the platter. Season the tomatoes and cucumbers with salt and pepper. Serve right away, letting people assemble their own wraps.