The Incomplete folder holds files as they're being downloaded. Once the download is complete the file is moved into your destination file. So LimeWire must have that Incomplete folder available to do its job. No point in deleting it, as it will always come back.

Don’t use the Incomplete folder as your download location. Use some other folder. Let LimeWire create and manage the temporary files in Incomplete on its own, and just forget that Incomplete even exists. Use E:\My Music or whatever as your download folder.