Although I don't think LW would "automatically" allow incomplete files to be shared, this is where you go.

Go to Tools>Options>Sharing, and find "shared directories". If your LW is sharing your incomplete files, in here you should find the folder which keeps them. Highlight the folder, and click "Remove".
It might be the case that,
1. when you first started up LW (and was asked about the files you want to share), you might have selected the folder named "incomplete files" by chance (in which case you just remove this folder), or more likely
2. at that time, you might have selected the folder which includes the "incomplete files".

Make sure that your "shared folders" don't have the folder named "incomplete files" within them.

Happy sharing.

Oh, and to the person who started this thread, no, you're not the only one who's annoyed. I'm annoyed big time especially at those who've renamed the incomple files and made it look as if they're completed.