Easiest way would be to connect via ethernet so you're networked.
I presume you forwarded a port to allow LW access right? If you're using LW on both computers then you'd need to forward a separate port number for each. Most modem-routers have internal NAT firewalls. So people would be having major problems uploading from either of you. One way to check is to open LW & leave it on at least 30 mins on each comp & then do this test:
Bug Report instructions & sample image If the report says False then you're firewalled for that port no. This is probably why you can't see each other.
What's more, for LW one separate port per instance of each computer is all that's necessary. BUT for games it's a different story. Many games require multiple ports to be opened. You'd need to check your game instructions for net use & see the advanced instructions about this to find out which ports are required to be opened.
SO what modem-router brand & model number(s) are you using? Perhaps I can direct you to some instructions on how to do it if there's any online.