Mix mayonnaise, lemon juice, onion and curry powder in a bowl and season with salt and pepper. Cover and chill until ready to serve. (Dip can be made up to 2 days in advance.)
Prepare a charcoal fire, let burn to a gray ash and set grill 8 to 10 inches from coals. (Or preheat a broiler and set broiling rack 8 inches from heat source.)
Cut sweet potatoes in half crosswise, then cut each half lengthwise and then into thirds to form fingers. Each potato should yield about 12 pieces. Place fingers in a large bowl, add oil, salt, pepper and cayenne. Toss well to coat.
Grill or broil fingers, turning often, until partially charred and soft enough to easily penetrate with tip of a knife, about 10 minutes. Remove to a plate and season with salt and pepper. Serve warm with curry dip.