In some non-US jurisdictions (such as the UK) it is allowable to issue conditional LUAWs, so the possibility exists that you would have a go-around of the landing aircraft.
I do not fly in Europe, but I assume that you normally only move onto the runway AFTER the landing aircraft has touched down. If the aircraft does not touch down (go around), then the LUAW condition is never met, so you do not move onto the runway. The controller would have to issue another LUAW (or departure clearance).
United States Answer
The example given is not a valid ATC instruction in the United States. A U.S. ATC should NEVER make a "conditional" LUAW. If a tower gives such an instruction, I would confirm it without the illegal conditional. If I heard a tower routinely making conditional LUAWs I would report it, because it is dangerous and a huge violation of FAA departure procedures.
You never line up and wait on the same runway which another aircraft is in the process of landing on, so the "go around" scenario should never happen. If, by some bizarre miscommunication, you think ATC is telling you to LUAW on a runway and you see another aircraft in the process of landing on that runway, you should say "[callsign] holding on [intersection] at [runway #], landing traffic in sight".
Note that it is dangerous and a serious separation violation for a controller to issue a LUAW when another aircraft is cleared to land on the same runway. If you hear a controller issuing such LUAW it should be reported immediately. Any landing aircraft must be landed and on the ground before a LUAW is given to a departing aircraft on the same runway.
If a plane is on long final (but has not been cleared to land), and you are given a LUAW on the same runway, the controller MUST inform you of the other aircraft and how far out they are. You may opt to refuse the LUAW based on that information. Under no circumstances will the other aircraft be granted a landing clearance, until you are off the ground.
If you are unclear about phraseology, you may want to review FAA Departure Procedures.