Facing this issue for a long time now. The only solution for me is to stick to an older version of precision X (5.2.4) Versions up to 5.2.8 are okay'ish, but still short input lag on startup. From version 5.2.9 and up the problem becomes very annoying, with input lag for like 30 seconds on startup.
I had this problem on windows 8.1 and as of today on windows 10. Clean install, minimum of 3rd party software etc. Would be nice if you can look into it, if you need more information, let me know.