DMCA takedown on forum thread?

A Digital Millennium Copyright Act notice won't work to get get the false review pulled down. Those are used to get copyrighted material removed from a website and have nothing to do with slander or false reviews. You may be able to get them to take it down if it can be classified as defamation or slander and is harmful to your business or character.

You woulf then also need to prove it was false.....

Almost impossible

You may need to find an attorney, legal assistant or online reputation management firm to help you with this coz DMCA only deals in protected copyrighted materials. Unfortunately, that's one of the drawbacks of the Internet, anyone can post a negative review about you or your company whether it be valid or invalid and sometimes there's very little to nothing you can do about it.

Unfortunately not, in principle: they don't cover defamation.

However, an approach to the hosting company may still be worth trying. Their attitudes vary. If they're willing to look at it at all, and to make a judgement, and if they decide it's "clearly malicious", they may choose to discuss it with their hosting client (i.e. the forum-owner). The reality is that they normally have something vague enough in their own terms of service which "might cover it", and may be willing to mention that to their client if they choose to. It's not completely impossible, anyway.

If neither the forum-owner nor the hosting company will help you, then you probably need a lawyer familiar with these things (but even that isn't necessarily going to achieve what you want it to).

Note, also, that if the person who posted in that forum is determined enough, even achieving the removal of the post/page/forum may still not turn out to be a "good solution" for you. People can find other places to post. There's a kind of "free speech with no responsibility and no quality control" element to the web, and it effectively protects malicious idiots, just as it protects anyone else - and predictably enough, they're sometimes the first to take advantage of that: the reality is that you can't always silence people who don't want to be silenced.

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DMCA won't be effective in your case, If it is false then it is a competitor who is trying to harm your reputation.

Tons of stuff on the internet is a lie, so are reviews. In theory (bill of rights) people should have the right to say and post what they want, but I'm sure that is less and less the case.