They can only get three years worth of damages, but there is no longer any type of time bar. In a 2014 opinion, which I consider terrible, the Supreme Court held that the 3 year statute of limitations in the Copyright Act is a limitation on the damages period, but not a time bar to bringing a lawsuit. Essentially, a copyright owner can sit back and wait for the infringer to start making a substantial profit, and THEN bring the lawsuit. The copyright owner can get damages for three years prior to the suit, and going forward.
In the past, accused infringers would claim "laches", and the copyright owner would have to provide some legitimate reason for waiting beyond three years to bring their lawsuit. That is no longer a defense to copyright infringement.
I said three years of damages, but that is looking backward. So its three years prior to the day the lawsuit was first filed, and maybe a little extra time if the copyright owner can prove that Led Zepplin somehow prevented them from bringing suit earlier. They will also get damages for sales after the suit was filed.
The case will probably settle now that the Court has ruled the case can go forward.