Can be crafted from any weapons workbench after the plan is obtained.
Behind the scenes
The light machine gun appears to be based off of the MG42, with a drum magazine and bell shaped flash hider. Rust is visible showing the wear and/or age of the weapon.
↑The editor ID of the light machine gun is shown to be "MG42", and the plan to craft the light machine gun is called "Plan: MG42 light machine gun", therefore it can be extrapolated that the weapon is indeed influenced by the MG42.