Apple has just released the first Java update for Mac OS X Lion, as well as Java for OS X 10.6 update 6 today, both of which patch security flaws in the previous version of the Java runtime.
Details are sparse about the actual contents of the update, but it is known to fix a number of coded security flaws, including one which could allow Java applets to run unauthorized code on your machine.a You can find full list of repaired Java vulnerabilities here (note: Apple is still updating the security file, so it may take a while for this to show for all users).
The update is available immediately through Software Update on the Mac.