Unfortunately, this problem is because the Light Machine Gun has not yet been added back into Fortnite — meaning no one will be able to complete this quest yet.
To keep the game interesting, developer Epic Games will cycle various weapons in and out of Fortnite, bringing certain ones back for a limited time or for specific events or seasons. The Light Machine Gun, specifically, has been kept in the vault a majority of time, since its ability to tear down structures makes it overpowered.
Source: https://www.distractify.com/p/where-to-find-light-machine-gun-fortnite