No word on the XB1 version just now, although perhaps there's no reason considering it's been out for a year on that system and I doubt anyone would want to go back and play it just because of improved imput lag:

As of version 1.04, however, this is no longer the case on the PS4 version. Developer Nixxes has heard our plea and completely eliminated the issue bringing the PS4 version in line with the PC and Xbox 360 versions of the game, neither of which suffer from this issue. It's revelatory change that greatly improves the game's combat by allowing players to more accurately aim its selection of precision weaponry. We had no issue pulling off headshots in version 1.04 versus our original experience which made the game much more difficult to play. Unfortunately, the original Xbox One version still possesses this fundamental problem a year on from release.

http://www.eurogamer.net/articles/digitalfoundry-2016-input-lag-fixed-on-rise-of-the-tomb-raider

Very good. Should have never existed in the first place. It is non-existent in the 360 version!