It looks like LibreOffice prompts you now when there’s an upgrade. I ran into a problem, though, when trying to upgrade on Windows 7.
When I tried the upgrade, I was told that I didn’t have enough permissions - even when I was running as administrator. I’d get an “error 1303: Installer has insufficient privileges to access C:\Program Files\…” and the install would always fail.
Even when I tried to take ownership of the files in that directory, I couldn’t. It was a puzzle. After a while messing about, I decided to nuke the whole thing from orbit. Finally that gave me a clue: when I tried to delete the files, some were left because a process was holding them open. (There were a couple of files - under share\config\soffice.cfg\modules\sglobal\toolbar) and whatever was running must have restarted at boot because it survived a reboot.)
That gave me the hints I needed. I booted into safe mode and deleted “C:\Program Files\LibreOffice 3.5” and its subdirectories. That worked, then I rebooted into normal mode and installed the 3.5.6 installer files. Now LibreOffice is upgraded and working again.