Core and seed the bell peppers. Cut each into six wedges, and place into a resealable plastic bag. Add the garlic and drizzle with olive oil. Toss, seal, and set aside to marinate at least 20 minutes.
Preheat an outdoor grill for medium heat, and lightly oil the grate. Stir the goat cheese and lemon pepper seasoning together in a small bowl; set aside.
Cook the peppers, skin-side-up on the preheated grill until lightly charred, about 3 minutes. Flip the peppers over, and carefully spoon the cheese onto each pepper. Close the lid of the barbecue, and continue cooking until the bottoms are lightly charred and the cheese is warm, 2 to 3 minutes.