I don't know if there's a way to enable LAN, sorry.
@paxicht
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I've also received a question about finding the CD-KEY if you purchased Reforged from Battle.Net. The thing is, I have no idea if it comes with a classic Warcraft 3 key, but if it is to be found somewhere: login to your battle.net account -> go to Games & Subscriptions -> scroll down, if there is a classic key, it should be listed there.
I've attached a screenshot of my account (obviously with removed CD-KEYs) for clarity -> see below.
If this doesn't work, i.e. the key isn't there, you have three options:
1. The launcher has an option to log in to your battle.net account instead of trying to type your key manually, you might try using that.
If you have a decent internet connection, available disk space and some patience, you can try doing what was described above -> install Reforged, try to launch 1.31, then remove Reforged and see if it remembers your activation (no idea if this will work, so only try this if downloading Reforged to try is really not a problem for you).
2. Contact Blizzard support and ask whether they can provide a CD-KEY for your Warcraft 3 copy. If they ask why, just say you've found an older installer and you want to play the game as it used to be

Anyway, no idea if support can help you in that way, but it really doesn't hurt to try
3. (Potentially risky!) If you don't plan on playing Reforged, see if they still offer easy refunds. Then try looking online for the original keys. I found some (cheapest from a trustworthy source was like 17,5 euro, saying in case you see some scam offers for a lot of money - don't fall for that), so you should be able to do it too.
Just
be warned - if you're doing this and want to play
only 1.31, you need just the
Warcraft 3: Reign of Chaos key, as it comes with Frozen Throne expansion by default, older versions will most likely require you to have both RoC and TfT keys. Also, classic keys do not allow you to play Reforged HD (but SD should be fine).
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Just in case - I had my old keys, so I didn't have to figure out how to get one these days. Thus, what I just said is not my firsthand experiece and I'd advise you to wait a couple of days (or read a couple posts below if you find this later) to see if someone with more experience in the topic didn't provide a confirmed solution
