Error: 'Access is denied LiteSpeed could not open the Backup file' (24535)

A similar error may appear when attempting to backup a database:

"LiteSpeed 2005 could not open the Backup file: (\folder\filename.bkp)
...
<ERROR error="5">Access is denied."

Verify the permissions for the login used to access the database. Verify the login has sufficient privileges to the server and directory for the backup file's destination. Verify the integrity of the hardware, such as the NIC or SAN.  

Verify  the login for the SQL Server service.   Is it different than the SQLAgent?     Unless you're calling LiteSpeed from the command line, it is using the SQL Server Service Account credential to access the destination location.  Verify that user access the destination, create, modify and delete files from that location.