In a small bowl, whisk together the garlic powder, lemon pepper, paprika, salt, brown sugar, thyme, and cayenne, if using.
Pat the wings dry and place in a large bowl. Sprinkle with the spice mixture, tossing to combine. Allow to sit at room temperature for 30 minutes.
Meanwhile, prepare a grill for medium-high heat (400˚F to 450˚F) for 5 to 10 minutes until hot. Scrub the grill grates with a grill brush. With a pair of tongs, dip a paper towel or clean rag in some vegetable oil (do not soak it) and wipe it over the grates. Prepare the grill for indirect heat. On a gas grill, turn off the heat on half the grill. On a charcoal grill, bank the coals on one side and leave the other side empty.
Place the wings on the unlit side of the grill, cover, and cook until fully cooked and starting to brown, 15 to 20 minutes, flipping halfway through.
Move the chicken to the lit side of the grill and cook, flipping occasionally, until lightly charred and crisp, 10 to 15 minutes. Transfer the chicken to a serving platter and serve with desired dipping sauces.
