After updating my LiveZilla installation I am not able to login anymore.
You probably uploaded the files of the (LiveZilla server) update to the wrong target folder.
When updating the LiveZilla server part you have to make sure that you upload the files of the LiveZilla server to the correct target folder (the folder you chose for the initial installation of the LiveZilla server).
Otherwise, the update will not be applied.
Note point 6. of the update guideline:
How can I update an existing LiveZilla (Server) Installation?: