Square Enix community manager Monkeythumbz has confirmed information on new Legacy of Kain games in development for Playstation 4 (cancelled) and PC (ongoing). However, he does so in context of clearing up rumors, versus Square making official announcements, so we don't get enough explanation or details for either game.
First off, based on data found and shared on NeoGAF, the Playstation 4 game's full name was Legacy of Kain: Dead Sun, and it has been in development for three years. Screenshots imply it was originally meant for current gen consoles, and clearly a lot of work has already been done on it, making the cancellation a genuine waste.
Among assets found for Dead Sun were pictures and video, showing off music, menus, cutscenes, environments, motion capture, voice acting, boss batles, and backstory all well in place.
In confirming Dead Sun's cancellation, Monkeythumbz provides little explanation aside from saying it was a case of the wrong game coming at the wrong time. He also generously shares more assets from the cancelled game.
On the flip side of things, on Eidos' own forums, Monkeythumbz confirms they are at work on a multiplayer online game called Legacy of Kain: Nosgoth. They make it clear the game is not an MMORPG, more in line to Unreal Tournament 2, is PC only, and is a different IP with a different story from Dead Sun.
It needs to be pointed out this information has surfaced and been confirmed in light of Eidos founder Stephane D'Astous recently leaving behind Square Enix, and complaining of problems with leadership, particularly direction for Enix. Dead Sun was made in the same work environment Thief was, so similar issues may have led to its cancellation. It is also possible that Square saw the financial toll they took with Tomb Raider, looked at Dead Sun, and saw the scenario repeating itself on much riskier next-gen launch situation, and decided to cancel for those reasons.
Whatever the case, the game looks like it could have been good, but we do have Nosgoth to look forward to now in the near future. You can check out the concept art Monkeythumbs shared below.