my STL has sometimes scheduled a regular TL as LOD for a shift to A) give them the experience and B) provide support to the actual LOD when we were busy/understaffed/had no other leaders in the building, but a non LOD TL would never be by themselves.
But my understanding is that only a Sr TL, ETL, or STL can be in the building as the officially designated LOD. TL key carriers can be in the building alone while it is closed however - and they would be acting LOD until the actual LOD arrives. One former SrTL I know who stepped down to a TL key carrier gets one LOD shift a month, but that was part of the deal she made with her STL when she stepped down - mainly with the thought that she would step back up as soon as her personal situation was resolved (transportation/childcare issues).
If the LOD had to leave the building in an emergency, however, they could hand off LOD duties to a regular TL, key carrying or not. I think they would have to contact either the DTL, STL, or ETL-HR ASAP.
One time, many years ago when I had to call in due to bad bout of pneumonia, I called and the operator transferred me to the GSA when I called in and asked for the LOD. When I asked for an actual LOD he insisted he was all that there was. I called back later when an actual LOD was in the building.