When I got to Tools->Options->LibreOffice, there is no Online Updates choice. Where are they hiding?
Online Updates is only available in version 3.5.0 under Help, Check for Updates
It is also activated by default, so only need to use the menu when you want to manually check.
When you want to change the frequency of the checks (or disable it completely without deinstalling the onlineupdate component), go to Tools|Options → LibreOffice → Online Update.
This option does not appear in my Linux Debian 188.8.131.52
if it doesn’t appear in a debian’s (or other distro’s) version of LibreOffice, then simply because the distro decided to not add that feature, as LibreOffice will be updated using the distro’s package management system.