The LiteSpeed silent install on version of LiteSpeed 4.5.0.00182 does not allow you to change the user.
To fully install the LiteSpeed application to ALL USERs, the following parameter has to be included in the command line:
Edit the msiexec.exe command line and add the parameter "ALLUSERS=2" to the command line. For example:
msiexec.exe /i C:\Litespeed2005.msi /qn SILENTINSTALLXML="C:\silentinstall.xml" ALLUSERS=2
The difference from ALLUSERS=1 and ALLUSERS=2 is that 2 will install to all users if it can, but if it doesn't have permissions to do so it will install just to the local user.
Option 1 will only install if it has the permissions to do so, otherwise it will throw an error.
It may be worth using an Administrator account.