There's a close to zero percent chance that a random person has plucked a completely fabricated lie about you out of thin air, for no reason, which a number of other random strangers are so convinced of, that it's given them the confidence to approach a complete stranger's family to request 'dirt' on this person.
There's obviously a ginormous back story to this around who these people are, what they're saying about you and why they're saying it, and if you can't/won't share any of it, you're not going to get any useful advice.
If they are completely rational, reasonable people who are genuinely mistaken or have received incorrect information about you, proof to the contrary from a legal firm, plus mention of your intention to sue, may indeed satisfy them that they're in the wrong and need to step back.
If you've somehow wronged this person and they've decided you're now their mortal enemy as a result, a legal letter will likely be seen as simply another shot across the bow in your ongoing feud.
If they're a nutcase who has infact completely fabricated a random lie about a complete stranger, they won't care if they letter is from you, your solicitor or Queen Elizabeth's ghost.
Threatening to sue someone when you don't have the means/intention to follow up on it could work, or it could backfire spectacularly - you'll have a better idea than anyone else here which it's likely to be OP.