LAN is Local Area Network. If you can't connect to said local area network, you can't use it.1
In other terms: The name of the wifi for both the hoster and player (both macs I assume) needs to be the same (i.e. both connected to same modem)
I'm not sure if you can use the neighbor's wifi as a stand-in (see the footnote below). Worth a shot though. (assuming consent is given)
As @Tas also noted in the comments, connecting the computers directly should work (with an ethernet cable). However if they aren't connected to the internet, things like skins probably won't show up.
1: LAN is weird. In my experiences, it usually means the set of computers connected to the same modem. But it can also mean the set of computers connected to the same internet cable/antenna/magic-receiver-thingy. (what the modem connects to) But most likely it means your wifi network in this case.