I need to kill him once so I can start While Guthix Sleeps but I've heard people say you need to complete What Lies Below to have access to him whereas other people say you just need to start the quest. I just need a simple answer.

 

Thanks in advance!

You need to do What Lies Below up until the point you unlock the tunnels east of varrock below the statue. I do not think you need to complete the quest, but given the quests short length and how late in the quest you access to the tunnels completing it is like 0 extra effort.

After all that I just realized I've done the quest already!

after the quest you have to do some sort of miniquest, where you have to follow or hunt that guy through the tunnel.

once you get to the "final room" you are in the room where you kill bork (also all following times you want to kill him).

Yeah it's called the Hunt for Surok