The key principle is that you get CLT when a bunch of random factors add. Which happens in lots of places.

In finance, the effects of random factors tend to multiply. So you get a log-normal curve.

As Taleb points out, though, the underlying assumptions behind log-normal break in large market movements. Because in large movements, things that were uncorrelated, become correlated. Resulting in fat tails, where extreme combinations of events (aka "black swans") become far more likely than naively expected.