The Lindy effect is a phenomenon observed within particular objects and abstract concepts where the current age of the object can be used to predict the longevity of the idea: a 2 year-old Lindy object is less likely to stay around than a 20 year-old Lindy object.
A Lindy object can be any non-perishable object, particularly ideas. Scientific developments are Lindy objects: a newly created piece of technology has a lower survival rate than a more established method, and the projected survival of a long-standing piece of scientific framework is increased by the length of time it has been in existence. For new theories, the few crucial years containing hype and funding and testing is the period of survival most relevant to the Lindy effect.
But in this case, rather than a scientific idea, the Lindy effect is being applied to a "Lindy truth" -- a statement whose truthfulness is suggested by the length of time the statement has been in existence. Let's put it like this:
If I think a phrase silently, or say it to an empty room, no information could be gained about its truthfulness. Except perhaps, some pondering.
But if I take that same claim and put it out into a room full of people, or perhaps on the Internet where people will see it and interact with it, then the continued survival of that claim indicates a decreased probability of that claim having some obvious flaw with it. After all, if people who intend to contradict it cannot find a problem with it, then the absence of that negation pushes the claim further from probable falseness. Without even considering the textual statement of the message, the Lindy effect can be used to attempt to predict its accuracy.
A semi-serious bit of online wisdom is that the fastest way to learn if an idea is false is to act as if it is true. To go into a public form and loudly declare it to be your real opinion, and dare the audience "Prove me wrong!". A Lindy truth is the enduring version of this test, the loud declaration which is heard and then not contradicted. The longer that a Lindy truth remains said without facing some utter takedown, the more it can be relied upon to be true. Of course, Lindy truth is not objective truth and it largely substitutes factuality for lack of controvertibility, but there is still some kind of filtering effect that removes falseness as it scales negatively with discursive longevity.
There is also the historical perspective: old adages and wisdoms seem truer and wiser to us than modern talk because only the most valuable and worthy inscriptions have been handed down to survive until modernity. There is an air of ancient familiarity that you feel when reading writings from civilization preceding yours by millennia, but which still seem wise and immediate enough to be applied to life today. Maybe these ancient poems and insights have survived so long because they contain a worthy idea or two.
Slightly meta note: at the time of writing, a lot of people who are using the phrase "Lindy truth" lack a definition of it, so this write-up itself is something of a Lindy claim: the longer this particular definition of Lindy truth goes without contradiction, the better the odds that this framing of the Lindy effect can be expected to be true.
Of course, there are also limitations on how useful the concept of Lindy truth can be. For starters, the claim being tested for truthfulness has to be read and understood by enough people for there to be a volume of discourse around it. If nobody reads a book, it doesn't get truer by the virtue of its publication date.
If the claim is about something considered "beyond debate", like theocratic assertions, or where contradiction is suppressed by law or force, then the continued survival of the idea is not drawn from its lack of flaws, but by the excessive might of its defenders. Its longevity is not supported by abstract worthiness, but instead by the real peril it threatens against those who do not accept it. Similarly, if a writing disappears from human history due to a burst pipe or a spilled candle, its demise was not caused by some essential falsehood, but by happenstance.
There is also the problem of continued propagation after being discredited. Take for example the modern conspiracy theory about Flat Earth: a 60ish year-old idea that has been empirically contradicted by scientific evidence and human observation since before its inception, but which continues to circulate despite damning proof against it. Lindy truth relies on the correlation between survival and merit, but there are surviving ideas that lack merit, and which we can expect to remain in existence for some time.
The modern person is afforded the powerful flexibility of both perceiving current reality and having access to an entire planet's worth of curated historical perspective, but it would be a mistake to interpret Lindy truth as a blind appeal to age as veracity.
See also: Memetic Evolution