Does the LiteSpeed Activation key change after an upgrade of SQL Server and re-install LiteSpeed.?
New license key is not required. It is advised that the LiteSpeed be uninstalled prior to the SQL Server update and reinstalled when the new version of SQL Server is running.
SLS Activation key generates from the MAC address, so it's hardware related, not software related. Changing the host name would only require Instance Config, not a new License key.