I have just upgraded my work machine (laptop) to Kubuntu Lucid Lynx (10.4) and have to say that I was mightily impressed with the ease of upgrade; 99% flawless. The one area where I did experience some difficulty was in running Zotero: Zotero Integration Error blared at me whenever I tried to add a citation. Fortunately, I had encountered this before and knew it was a problem regarding OpenJDK and IceTea. Indeed, a quick google search turned up the answer, which I will quote here, with minor alterations to account for the final versions. Open up a terminal and type, line by line:
sudo echo 'deb http://archive.canonical.com/ubuntu lucid partner' >> /etc/apt/sources.list
sudo apt-get update
sudo apt-get install sun-java6-bin sun-java6-jre sun-java6-plugin
sudo update-alternatives --config java
sudo ln -s /usr/lib/jvm/java-6-sun/jre/lib/i386/libnpjp2.so /usr/lib/mozilla/plugins/
Go into OpenOffice. Go to Tools -> Options -> Java and select the Sun 184.108.40.206 runtime. Close OpenOffice. Then, in Firefox go to Tools -> Add-Ons. Go to Zotero OpenOffice Integration and click Preferences. Reinstall the OpenOffice extensions from there. Fire everything up and you should be up and running!