The NRA has one already going. I personally know one of the plaintiffs.
I know there are some gun shops that are suing as well, but I have not heard of any state legal action.
I suspect that is because this stupid law is toothless, since FFL sales are already reported via the NICS check.
Still, I would like to see a legal response from the states to protest border states being singled out for state specific federal restrictions.