It looks like the /Applications/LibreOffice.app/Contents/Info.plist shows
a "false" value for NSHighResolutionCapable causing it to not use retina
text rendering.
You need to change this:
<key>NSHighResolutionCapable</key>
<false/>
To this:
<key>NSHighResolutionCapable</key>
<true/>
Note: if you want to fix an existing copy of LibreOffice, you need to update
the Info.plist, then rename LibreOffice.app to something else like
LibreOfficeRetina.app, open the application and see that retina works, then
close and rename it back to LibreOffice.app. I'm not sure how else to clear
the cached value but that works.