Yes ... move the entire folder .. important to keep the download.dat & download.bak files within that folder, else the incomplete files will not mean anything to the new limewire. Those are the download history files.

However, and this is VERY IMPORTANT, install the new LW, then if it opens ok, close it. Then replace the new incomplete folder with the old one. This MUST be done whilst LW is closed, else the download history files will be zeroed. Make a back up of those download.dat & .bak files just in case.