Squeeze lemon juice into a small bowl, and slowly whisk in olive oil. Whisk in salt, paprika, white pepper, and garlic powder. Split lobster tails lengthwise with a large knife, and brush flesh side of tail with marinade.
Lightly oil grill grate. Place tails, flesh side down, on preheated grill. Cook for 10 to 12 minutes, turning once, and basting frequently with marinade. Discard any remaining marinade. Lobster is done when opaque and firm to the touch.
