Trademark infringement and dilution. By pretending to be In N Out they confuse customers into thinking they are buying from In N Out directly.
There is a first sale doctrine in Trademark, but it might not (probably?) won't apply here. First, courts have found that not all reselling falls under first sale if the products aren't exactly the same. Here, by delivering they are serving different food because it gets cold and soggy. They could also argue that In N Out doesn't provide delivery service and this place is selling that service using In N Outs trademark.
The damage to In N Out is brand devaluation. People might think that In N Out sucks.
A clear example is: You can resell macbooks. You can buy them, sell them, even repair them.
But you can't set up a fake Apple Store that looks like a regular one.
Doordash is argue they are doing the former, and In N out will say the latter.
Apple store is an interesting example. If you put up a giant flyer "Macbooks sold here!" but stripped them for parts, replacing the RAM and SSD with slower, cheaper versions, you might expect angry letters from Apple too.
That's the trademark side of the case, and yes, In N Out could probably successfully argue that usage of their logo implies endorsement and/or is likely to create consumer confusion and that it's therefore a trademark violation. That's pretty easy for DoorDash to put to rest; just stop putting In N Out's logo on the site. A few good, highly-visible disclaimers would probably put any remainder of a trademark claim to rest.
A modified menu would be tougher. You can argue that there may be copyright infringement, and that may be valid to a limited extent, but DoorDash could put up a version of the menu that wasn't copyrighted, as its heart, menus are factual arrangements, and facts are not original creative works subject to copyright (though a specific arrangement of those facts may be). In N Out could also claim that there's trademark infringement if DoorDash is using trademarked food names, but I think it'd be a harder argument to win, since DoorDash can argue it's a nominative use.
I can understand the factual part, but only if they didn't alter the prices. They'd have to at least mark it clearly that they're charging on top of the prices some amount.
They don't need legal standing. They're a big company, and big companies sue people they don't like into bankruptcy. The basis of the claim only needs to look vaguely possibly meritorious for the lawsuit to be forced through the uber-expensive court circuit.
Only way to avoid being sued into bankruptcy after you've pissed off someone big enough is for your company to be doing dozens of millions each year at minimum, and thus, have the resources to tolerate the associated legal fees. If you make someone mad before this happens, expect to be forced to shut down.
There is a first sale doctrine in Trademark, but it might not (probably?) won't apply here. First, courts have found that not all reselling falls under first sale if the products aren't exactly the same. Here, by delivering they are serving different food because it gets cold and soggy. They could also argue that In N Out doesn't provide delivery service and this place is selling that service using In N Outs trademark.
The damage to In N Out is brand devaluation. People might think that In N Out sucks.
A clear example is: You can resell macbooks. You can buy them, sell them, even repair them.
But you can't set up a fake Apple Store that looks like a regular one.
Doordash is argue they are doing the former, and In N out will say the latter.