Indeed, the application doesn't appear to be available from anywhere on the web. If it was previously available, right now there is no download possibility. I've searched the web and all the related websites.
However, as far as I know, LG has other tools you can use with your phone, and I believe they have the synchronization tool bundled with other applications.
Just check the downloads for your phone to see all the available alternatives: http://www.lg.com/us/support/cell-phones