Hi Stephan,
I think I can help. &: )
First off: if the LiveUpdate policy is correctly created and applied to the client group in the SEPM, all the SEP clients should automatically receive the settings directing them to use the internal LUA address. There is no need to also use the settings.hosts.liveupdate file. (Those hosts files will work with managed clients, but it is easier and better to just configure the seeetings in SEPM policies.)
So: have you 100% confirmed that the LiveUpdate policy is correctly created and applied to the right group-? Feel free to add screenshots to this forum thread, if you like: admins can probably spot any errors pretty quickly.
Are these SEP 11 or SEP 12.1 clients? If it is SEP 11- check the settings.liveupdate file of the SEP clients in that office. What is configured there? Examine the log.liveupdate. What exact errors are seen when they try to update? Again, feel free to add the info from those files to this thread.
LUA 2.x is a fantastic tool. I know a good bit about it- please add your info to this thread and let's see if we can't get to the bottom of the problem quickly. &: )