LAS Tower Local Controller reported an NMAC when a Runway 19L arrival unexpectedly initiated a go-around and flew over the top of an aircraft on short final to Runway 8R. The reporter states published procedures in place for this arrival configuration do not adequately protect for this occurrence.

Narrative

Configuration 4 at LAS has been on ongoing issue. There have been many near misses and the NTSB has come out to review them several times. This is a known issue that needs more attention or a mid air collision is inevitable. Recently; our management and NATCA team came out with a revised procedure to try and mitigate these near misses. What they did is commendable but today I found out it doesn't work. L30 [Approach] apparently makes no attempt to try and sequence these aircraft to the intersection; they come over tied all the time. What our leadership team came up with is 1 mile is required in front of [Runway] 8R arrival or we have to send the [Runway] 19L arrival around at a 2 mile final. The other requirement is that you need to be established behind the 8R with your 19L arrival. No mileage is required; you just need to be behind them. Today while following that procedure I was behind the 8R arrival and Aircraft X went around on his own just prior to the runway threshold. He passed over the top of the 8R arrival by approximately 400 feet. I expedited his climb as soon as he said he was going around. Had he gone around 5-10 seconds later; I believe these aircraft would have collided. They will say I was maintaining visual separation and that it wasn't a loss. I had no control over that situation; no out; no altitude separation and nowhere to turn the aircraft to avoid a collision. I just called a traffic alert and prayed it would work. This is not air traffic control. The arrival rate needs to reduced to allow L30 to sequence aircraft to the intersection. With that; L30 needs to create its own procedures to ensure mileage can be maintained between the intersection arrivals. Mileage needs to be established behind the aircraft. It's 1 mile in front and 0 miles behind. It doesn't matter which one is in front; we are trying to avoid a collision. I would highly suggest increasing the spacing in front and behind to more than 1 mile. When an aircraft is going around; their speeds can be unpredictable and 1 mile can be lost quickly.