This is for advanced users only...
Basically, you need to have a computer running LST Server offsite and a computer running LAN Speed Test (Client) onsite. The offsite router needs to have port 4456 open and forwarded to the computer's LAN IP (shown in LST Server window under Server Status) that is running LST Server. Then on your onsite computer, you would enter the WAN IP address of the offsite network (should be the WAN IP address shown under Server Status on LST Server at the offsite location).
For example... hypothetically, at work, I have a computer that I run LST Server on. First, I make sure that it is using port 4456 (under Server Status window on LST Server). Also under the status window, I see that the LAN IP address is 192.168.0.10 and the WAN IP address is 123.132.10.12. On my router (here at work still), I go to the port forwarding option and open port 4456 and forward it to IP address 192.168.0.10. I have to keep this computer on with no sleeping or hibernating during the time that I want to do my testing from home. Now, at home, I start LAN Speed Test and enter the WAN address of the computer running LST Server in the 'Folder or Server IP:' window (123.132.10.12) and begin the test. First time running, I make sure that my settings are set for slower connections (ie. 'Test Packet Size' = 100 KB and 'Number of Test Packets' = 5). If all is set up correctly, the test should begin and complete as though you are doing a LAN Speed Test (only slower). You can adjust your settings with larger Test Packet Size and higher Number of Test Packets as you would like once you see how long it takes to test over your internet speed, etc.