Yeah... I don't consider myself to have "internet fame" but I suppose I'm well known enough in certain large communities that I've managed to attract these people. I've ended up leaving the communities where these people are active, but I have seen evidence that they continue to spout lies about me there. I often wonder if people just take what they say at face value. The urge is to stay in those communities and correct the record at every opportunity to defend my reputation, but that takes a huge amount of effort and sanity to deal with. Is the advice in these situations to simply ignore and forget?

In the first case, the community is healthy. In that case, someone spouting lies about someone who isn't even there anymore is going to look rather odd, especially if you had a history and a track record there. It has a good chance of not getting much traction, and it might get some pushback from the community. In this case you have a fair chance of being able to successfully leave your reputation in the community's hands.

In the second case, the community is toxic. The lies are believed, and even amplified by others. Your reputation there is toast. You could go back and fight for your reputation, but if you did, you'd be likely to lose, and the attempt would eat up your time and emotional stability.

In either case, just walking away and ignoring it is about as good a strategy as you can find.

Note well: I am a random nobody on the net. I don't have a reputation online, except under pseudonyms, so I am talking about what I do not actually know. (Yes, I am aware of one person online who defamed my real-life identity. They were obscure enough, and their rant was obviously unhinged enough, that I felt no actual harm from just ignoring it.)