Last time I tried LAN mode a year or two ago it was working fine as I recall, except that it would desync me more often than Reforged. I assume the desyncs were due to some programming issues on the old version and maybe some Win10 compatibility stuff, where some stuff that used to be consistently calculated on all hardware might be more variable now, perhaps. We also had the unlucky case of hitting a reproducible desync in that version where an illusion with evasion who gets attacked on a bridge instantly causes desync/end of game or something like this. I tried recreating the scenario and it would desync every time, although the friend's computer I was testing with did not have Reforged and I was not going to force that on him to see if Blizz had fixed it at the time.
I know it's a bit of an obvious question but have you checked your firewall settings? There is no more support for the old version anymore but I am not aware of any reason why it would have stopped working, so I figure having it not work is probably a configuration issue on your side.