I know the size limit was increased, but not sure what it is now. I think it is larger than 2 GB rather than what the 2nd link suggests. (this also takes into consideration for torrent files which can be very large. Torrents were only introduced into LW in recent two years or so. Bittorrent was introduced in the LW Beta 4.13 on 10.30.2006, & introduced into the main version LW 4.14 on 07.26.2007.)

Perhaps a better way of transferring the file is sending your friend a magnet link of that particular file; How to use Magnet Links & Direct Connect. ie: right-click the file in your Library window, then choose to get Magnet details for it. Then send those to your friend. They simply copy-paste that detail into their browser & if LW is the default magnet handler, then LW will start downloading or attempting to download the file.

hmm ... I need to find out about the file size limit. I just added several 4 GB files to my shares over past few days.
Only reference I can find on the LW update history page is file sizes for share increased to 1 TB (4.13.9 (06.29.2007)).