Comment 30 for bug 820118

I saw this happening in version: LibreOffice 3.4.4 OOO340m1 (Build:402) (current in Ubuntu Oneiric).
I found that the tooltip background and foreground colours obey the KDE text colour settings Tooltip Background and View Text, respectively.
(These are the names as listed under System Settings -> Application Appearance -> Colours -> Colours tab -> Colour set: Common Colours. They seem to have different names depending on where you go to edit them.)

I have since upgraded to the current Oneiric version in ppa:libreoffice/ppa (LibreOffice 3.5.0 Build ID: 350m1(Build:13)).
With this build, the colours are taken from Tooltip Text and Tooltip Background colour settings as expected.

So, someone has fixed this bug, and the Tooltip Background/View Text settings provide a workaround for older versions.
Of course, a backport would be nice, if any package maintainers are watching... ;)