In the HI policy, it should be a simple matter of telling the client to run either LUALL.exe (SEP11) or SepLiveUpdate.exe (SEP12.1) in order to update from the LUA.
This requires that the LU Settings policy assigned to the client allows a liveupdate session to be run, and that it tells the client about the LUA.
You should not need to use the "Download a signature file" option, as this is typically used to point the client at an internal location where the Intelligent Updater has been pre-staged (which would then be called with the %F% function).