Why have my permanent marker pens run when I varnished them?

Don't worry about your current rock, as long as it can still be read, it will still make someone's day when they find it.

There are a number of reasons why this could have happened, but let's concentrate on the more obvious reason first, as this one is from experience.

I use spray lacquer and, when I first started creating rock art, I was eager to get my rocks out there and fast! So I sprayed too much on the rock in one spraying.

The best advice I can give is ... fine or very thin coat of first, allow to dry and then add a second coat. This will help prevent the same thing happening again.