wishZor, considering the archived log files you sent are empty except one then yes they are of no use.
Second It could be that your config files got corrupted some how such as a friend of mines did recently.
This would not update nor delete anything either etc.
Be sure you have Jdownlaoder closed for the following process:
I had to go into their app and do a right click on it to show contents.
Then under Contents/Resources/Java/ directory is the config folder.
Inside that folder there should be four files.
database.log
database.properties
database.script
version.cfg
It is safe to delete all four of these files (do not delete the folder itself though. Trash the above four files and be sure to empty the trash. Then restart Jdownloader.
When you restart it it may take a bit of time to connect but it should connect to the update servers and start updating what it needs to.
If for some reason the update does not start then you may need to try closing and restarting another time and as soon as it is restarted select the check for updates globe at the top right set of icons. You probably will see that updates are already in progress ... you may have to have some patience for the process to finish but it should within 5 minutes maximum.
If for some reason the above does not work at all then you have to go into terminal and drill down into the app itself to execute the command ""java -Xmx1024m -jar JDownloader.jar"" which is also in the root of the Contents/Resources/Java/ directory.
I refuse atm to run Lion as it is still unstable for production and as such I [S]have no idea about which version of Java update you may be using but be very careful as Apple quit supporting Java as they had done for so many years with this update of Lion also. In Lion, Java is no longer preinstalled, but rather is available for download as an optional package after install or before opening an application that requires the Java runtime. I know many though that have updated and they have no real problem with Jdownloader to my knowledge other than the occasional hoster burp or bad connectivity from their ISP to the hoster's ISP etc.
If needed you may wish to try to run a restore of course and or the permission repairs and also check the disk for errors.
One may also wish to review and report problems with Java and Lion here "**External links are only visible to Support Staff**
One may also have a corrupted Java install and as such may need to reinstall the update again such as spoken of here "**External links are only visible to Support Staff** etc.
Apple has also released the latest 10.7.3 update to developers on December 2, so maybe if there is an issue it will get fixed there.
spnyc and others ... first there is not a function delete on the Mac. considering this is Java and the interface for the Mac Java is not near where it needs to be although there I think is at least one Mac programer on the team, one needs to use the ctrl key and mouse click or a right click if they have a mouse attached for the drop down menus to pop up. One has to select either the folder/package or file within a folder/package and do the right click to see which item in the dropdown list they wish to use.
as bellow