What reference sound you shooting for? Neutral, warmish, a detail-monster? End-game type dac/amp setup or something to dip your toes in?
I've not owned an Audeze yet but I do have the Edition X from Hifiman, I have heard the LCD series like a bit of juice.
Perhaps, check out something from JDS labs, Schiit have some price/performance stuff there that could go well with your LCD-X. There are fans of Audio-GD products as well that could partner up well with your headphones.
I do believe Audeze have their own dedicated amp as well, if you're wanting to go down that direction.
Hope this helps.