I don't think you would go wrong with any of the headphones you're considering. I have not heard the exact models you are considering, but have LCD-XC (closed back version of LCD-X), Hifiman HE-560, and Sennheiser HD800 (not HD800s). Audeze and Hifiman have a fairly similar sound signature, with Audeze being just a little warmer and maybe a little better in the bass department. The HD800 is a very "clinical" headphone, not really bright, but they can be too detailed for some. From what I've read, that was tamed down a bit in the HD800s.
So the first thing you have to consider is what kind of sound signature you like.
Then you need to think about things like comfort and amplification. Some of the Hifiman headphones can be pretty hard to drive, the HE-560s are. The HD800 is lighter and more comfortable to me than any of my Audeze or Hifiman headphones.
If you want to put together a really nice rig, take a look at Sony - MDR-Z1R headphones and the TAZH1ES amp.