While they were only available to be bought by the corresponding faction from the vendor, they could be traded and sold on the auction house by either faction. And once learned they could be summoned by either side.
Currently though they are faction locked and you get an error message if you try to summon the opposite faction’s lantern. Intended or an error? If intended seems silly after at least a dozen years of being able to have both.
My guess is that some individual at Blizzard noticed that, omigod, we’re letting players summon pets that weren’t intended for them.
Of course there’s also all the current bugs with knowing in advance what drops you’re going to get from Shadowlands pet WQs. The lantern change could just be an unexpected result from all the changes being made.
At least either faction can cage each lantern for trade or sale.