When you create a new maintenance plan (MP) in Litespeed, the authentication for the Local server connection is automatically set to connect using the authentication type with which the server was registered in Litespeed. You can change the authentication from windows to SQL Server authentication but once the connection is saved as SQL authentication type, you cannot reverse it back to Windows.
You should always be able to switch between windows and Sql server authentication.
To change connection from SQL authentication back to windows authentication, delete the SQL server registration and re-register it again using Windows authentication. Re-create the maintenance plan.
CR 99516 created to address this issue.
This has been fixed in LiteSpeed version 7.1 and higher.