The first thing I did was run
This did NOTHING to resolve the problem. Apache still would not start as it kept stating that the license for litespeed had expired even though litespeed was no longer able to start as it had been removed.
The ONLY way to resolve the issue was to install the standard litespeed server at a different port then switch to apache and then run the uninstaller. So something is wrong with your uninstaller somewhere and something is definitely wrong with the way the trial expires. If you do not think so then I suggest the following.
Amend your info regarding the trial to:
If litespeed is not removed before the end of the trial it will disable your webserver. Switch back to apache is not done automatically. This may make it difficult to switch to apache resulting in your domains being offline as this will also disable access to WHM on a cpanel server.