Some users reported an issue where the installer did not work properly on Mac OS X 10.7. We are currently working on a fix.
In the meantime it's really simple to fix the issue locally:
Step 1: Open application "Java preferences" in folder Applications/Utilities (You can also use Spotlight).
Step 2: Hit install Java
Step 3: Install BackupGoo.
That's it. It won't take too long, and installation of Java is 100% automated and simple :)