When can an aircraft be authorized to LUAW if another aircraft has been cleared to perform landing options?

The option that states an aircraft can be authorized to Line Up and Wait (LUAW) once an aircraft starts its takeoff roll is correct because it indicates a specific moment when separation can be effectively maintained. When an aircraft is cleared for takeoff and is rolling down the runway, it is in a dynamic phase of flight where the potential for conflict with a LUAW aircraft is minimal, provided that the controller ensures sufficient spacing and awareness of the situation.

In air traffic control operations, maintaining safety is paramount. Therefore, LUAW may be acceptable in scenarios where the traffic flow can be managed without compromising safety. When the takeoff roll has commenced, the aircraft on the runway is considered committed to its takeoff, allowing controllers to use their discretion in managing the runway's status safely for those awaiting departure.

Other situations that do not align with safety protocols would prevent authorization for LUAW, which is reflected in the other choices presented.