You should be able to yes. And the download speed should be very fast if it's on a LAN. With LW 4, such a download would show up as a blue colour signalling it was a LAN download. With LW 5, I'm not sure if it signals anything about it being LAN at all.

One easy way to pass such files across is for the one who has the file in their shares to create a magnet link & send that to the person who wishes to download the file, once the download starts, the downloader could then browse the rest of the sharer's files. How to use Magnet Links. There is also the Friends option with LW 5. I cannot give you specific details how it works since I've never tried it.