Yep, one problem with Direct Connecting or using Magnet Links, is that it gives that ip the computer is using at that time. But many people's ip's change every few days or even every day if they are dynamic ip's. So you need to recheck your ip just in case. LAN's will connect very easily & will give a blue connection sign for quality ... you will notice when you see it, & very fast when transfering files.

LW will give your ip at the time when you choose Direct Connect search type. If you don't see it, it means you have a firewall issue in which case you will have great problems using direct connecting type. AFAIK direct connect will not work if you are in that scenario. On a LAN connecting between each other might be different I am not sure.