Of course you can setup LimeWire to do that. If you can, try getting the latest LimeWire from cvs at www.limewire.org or the latest AquaLime from www.unitethecows.com.

If you have are connected to the internet, while you want to use LimeWire over LAN delete all quick connect hosts from preferences->connection. (No need for that if you aren't connected to the internet anyway). If you have the latest AquaLime or LimeWire from cvs, you can go to preferences->filters->hosts instead and enter *.*.*.* into the 'filter hosts' text field (to block all ip-addresses) and enter your local subnet (usually 192.168.*.* and/or 10.*.*.*) into the 'allow hosts' text field to allow only connections from your LAN.

Set your speed at preferences->speed to at least cable/dsl (also make sure that ultrapeer capabilities aren't disabled).

Also make sure, you know at least one of your computers' ip-addresses. Try manually connecting to the one ip-address that you know (the computer with that address will probably become an ultrapeer then).

Now you should be able to search for each other's files. If you have the latest LimeWire or AquaLime you can even browse each other's shares.