I vaguely remember a video showing this. It was done split screen with one side being a scene from TOS depticting Kirk and Spock having a conversation in a turbolift on their way to the bridge. The other side was a schematic of the Enterprise with a dot running along where the location of the turbolift would be.
The video shows that the lights in the turbolift change directions as they would if it was really moving through the ship. It was meant to show the level of detail that Gene Roddenberry put into the show.
Since I can't find the video I am unsure of the authenticity. Was this actually a consideration during production?