According to the widely-cited "Lindy effect" Wikipedia page, the future life expectancy of a technology or an idea is proportional to its current age. However, this is a non-scientific and statistically-invalid claim, which is often used by Bitcoin maximalists to back their claim that Bitcoin is more valid because it's been around for longer.
Simple Analyses
Let's take a look at Google Trends worldwide since 2004 for the phrase "DVD" (does anyone still use those?).
Interest in DVDs has been diminishing ever since Google Trends has been collecting data. Clearly, DVDs are on the way to their death-bed (if they're not there already). Yet, according to the Lindy Effect, the life expectancy of DVDs should be increasing year-by-year over their existence.
This isn't just for DVDs: any technology that has ever died has contradicted the Lindy Effect for at least half its lifespan.
Indeed, we can repeat this example with any dying technology. Interest in the word "fax" has been diminishing over its lifespan, in contradiction to the Lindy Effect.
The same is true for "iPod"...
"Bitcoin"...
... and every potentially dying technology out there.
That being said, in complete absence of additional information, the Lindy Effect can be a useful measure. However, given the massive abundance of data on technologies like Bitcoin, Lindy is no longer a useful measure.
In isolation, it's easy to believe in the Lindy Effect. "Bitcoin has been around for longer, so it'll be around the longest." It might sound right, because there's already a familiarity with Bitcoin as the most common cryptocurrency, so you expect Bitcoin to last to some extent. However, all believability goes out the window if I suggest that "newspapers have been dominant the longest, so they'll continue to be dominant for consuming content."
A Medium article discusses the statistical fallacy of the Lindy Effect, with the most common rebuttal being that the Lindy Effect is only useful applied to some technologies. That is a fallacy of selective attention, or in simpler terms: cherry picking. You can't just find a few example of where the Lindy Effect holds true, and say "see, the Lindy Effect is true."
It's like saying that global warming is a myth because you're cold, here, right now. One example is not evidence for or against a greater theory.
The Lindy Effect Theorizes That BTC = BCH
Finally, the Lindy Effect describes technology, not applications built on the technology. For example, blockchain is a technology, and both Bitcoin and Bitcoin Cash are applications of blockchain technology.
The underlying technology is the same, meaning that the Lindy Effect theorizes the same life-span for Bitcoin Core and Bitcoin Cash.
Indeed, the Lindy Effect even theorizes that other cryptocurrencies will have a longer life expectancy than Bitcoin. For example, Monero uses some tech that predates Bitcoin Core, such as ring signatures and range proofs.
Monero should then have a longer life expectancy than Bitcoin (but only if you believe in the Lindy Effect). Ultimately, the Lindy Effect is useless in predicting the validity of cryptocurrencies for a number of reasons.