Hello Andrew,
You can run Fiddler on your computer while using the Geo Map in Lumira Desktop. Fiddler will capture the HTTP requests and response from Lumira Desktop, and it will show you all the details including the header, body, status code, URL etc.
If you save the Fiddler trace into a *.saz file, you can then send it to your network admin so they can examine it.
You can download Fiddler from: Fiddler free web debugging proxy
Regards,
Alan