Then you have a problem...
Well, I feel that this is much more an issue of a server and network setup than of the web application like Limesurvey.
The normal setup is to have Limesurvey installed on a server that is accessible via the internet, so you access it via the domain.
For sending emails, Limesurvey usually uses as a base the URL you are logged in with. There are options to change that (as you did), but I have no experience with that.
Maybe some of the developers see this and can help out. So there is no way for you to use the Domain that is used for external access? If you login via this domain into your LS administration (if this is possible and not blocked by your network admin!), then you should be able to sent the emails with the correct URL to the respondents. But I assume your admin doesn't allow this option from within your local network, right? Otherwise you probably wouldn't ask.
Let's how that one of the developers shows up, they might be able to shed a little bit more of light on your options.