Barnum, as VB said, Yikes!. You're definitely going to have to free up some space on that internal (probably C:\ ? ) drive. Running that close to full is possible/likely to cause (weird) problems with almost everything.
If there's any unnecessary data living on that drive, you may want to offload it to the external drive. If you can get enough data moved, you may not have to move any application program files. Is your LR Catalog located in the standard location of \My Documents\My Pictures\Lightroom ? Is My Documents located on that internal (C:\) drive?
It may be that one possible solution to the the over-stuffed disk is to move the LR Catalog itself to the external drive.
Before we do anything else, make sure you have good backups of the LR catalog(s). While the following is what I'd do if I were in your shoes, you may want to wait on any commentary to my post to arrive, before you start anything.
I'd recommend creating a 'LR Catalog' folder on the external drive, and copying the contents of the LR catalog directory listed above to it. To open that catalog, you can simply double-click on the *.lrcat file, in its new location, or hold down ctrl as you start LR in the normal fashion. That should give you a dialog allowing you to select a catalog to open, you would then navigate to the catalog which has been moved to the external drive. (As a side note, you can use either of these methods to test your LR catalog backups to ensure they've been captured and written properly as well.)
When you have that copied catalog open, exercise it fully to make sure it's functioning properly. When you're fully satisfied that it's working properly, (or at least, no worse than your current problems) then you can delete the existing files in the My Documents location. You might want to delete the preview cache located there as a first step, which should free up a lot of space, and is easily reconstructed if you decide you need it back.
I'd begin with other non-critical data first, if you can, though.
