My friend and I still have copies of Age of Empires: Age of Kings and we have installed it both our laptops.
Is it still playable over LAN?
If you mean the old Windows 9x game, then... kind-of....
It uses an older style of LAN networking that is not used these days (I think it is IPX), and you would have difficulty installing and setting up the computers to use it. The setup required for it was picky, and I mean on Windows XP -- back when you could still easily install it! (EDIT: "easily" meaning the drivers, not the extra steps to take)
If you have Linux installed somewhere (or a modern-ish Mac) and have the Windows 9x CD of the game... I don't know how well it will work with PlayOnLinux (free) -- (PlayOnMac for Mac users, also free)
Age of Empires 2: The Conquerors ONLY:
There was a custom 1.0e patcher for AoE2:TC made by a group (that could switch between that version and 1.0c), but I have no idea where it is located, and since what that 1.0e can do (allowing no CD in the drive), I cannot recommend it, and especially not link to a download... ... who knows if there even still exists a download to that patcher which isn't malware!
Alternate solution (chosen by the asker when offered): Buying the Steam remake which they found on sale.
I played the old version of AOE II with expansion for a long time over lan, including Windows 10. The only problems I ever had starting the game (ranging from Windows XP to Windows 10) was administrative rights for the network tool AOE II uses and fire wall blockage for which you just have to say 'Allow' and be done with it.
Make sure everybody has version 1.0c and maybe check compatibility mode.
To be honest, I have more problems with the steam version than the old version for multiplayer. The old version loads multiplayer save games nicely, but I never got that working for the steam version. I also have more problems with network stability when playing on steam compared to the old version.
download gameranger and then you can play both aoe and aoe2 easily online.