See, actually using the word "cover" in the ability description would steer readers to this logic alot quicker. I see what you're saying that the Lightfoot have a special ability to hide when they only have half cover granted by a larger creature, where normally you'd have to have total cover (be unseen.)
I'm not necessarily worried about how to defeat the tactic. I'm not decrying the ability as overpowered or broken. I'm just trying to get it to make sense in my head. As others pointed out, if the fighter buddy is actually in melee with the target, you have advantage anyway, hidden or not.
The Hide action isn't tied to the movement, but a Stealth roll can be. It's the "and unheard" part (fka "Move Silently") of being hidden. Plenty of examples in the rules, such as using Stealth in exploration, or the Supreme Sneak ability of a rogue. Assuming you successfully used the Hide action behind the tree first, as long as you keep the tree between yourself and the orc as total cover, you continue to fulfill the "unseen" qualifier. But if you move, you risk breaking the "and unheard" part. So I'd call for a Stealth roll to *remain* hidden.