Slander, triangulation, character assassination
There are several ways how the narcissist employs their lies and projections, and the goal is always to turn others against you in hope that they won’t try to figure out the truth.
One of the ways to do that is triangulation. In psychology, it means controlling and manipulating communication between two parties. It is related to gossiping, smearing, and slandering, where the narcissist spreads false information around. A more extreme version of all of that is character assassination, where the lies are much more severe and damaging.