According to their press release, "The Air Transport Association of America (ATA), the industry trade organization for the leading U.S. airlines, today filed a lawsuit against the Federal Aviation Administration (FAA), responding to its decision to auction slots."
There is ample legal history demonstrating that "slots" are administrative creations of the U.S. DOT, not the private property of the airlines. If the airlines believed their own rhetoric on this issue, there would be no need for Sen. Schumer's bill to take this legal authority away from the FAA (the aviation arm of the DOT). But the airlines support this legislative effort. Likewise, about eight years ago when Congress irresponsibly removed the cap on the number of slots at the New York airports, not a single airline filed suit over any "taking" of its property. So one can only conclude that ATA's current lawsuit is an act of desperation, rather than being based on a strong legal position.
As I wrote last week, the plan to auction off this slot is a good start.