-I tried the LCD-2 (basically same-ish design as the LCD-X, though with a slightly higher impedance) with an O2 a few months ago; it worked a charm and had no problems whatsoever driving the headphones to way beyond comfortable listening levels without any sign of running out of oomph.
No discernible background noise (whether it was run from batteries or a wall wart), and overall an impressive piece of kit.
My one gripe with it would be that the controls feel a little flimsy - note FEEL; I have no reason to believe they wouldn't stand up to normal use for years. They just don't feel as substantial as the controls on, say, Tascam gear (manufactured for pro use and a knob will easily set you back as much as a complete O2...)
Bottom line - I'd buy an O2 in a heartbeat if I didn't already have the amps I need.
Thanks for the input OddE, I discovered that even my iPhone 4S is able to drive my LCD-X although not to the level of my Cayin C5. Never the less, I'm on the lookout for a decent but affordable amp to pair with my LCD-X after having spent quite a bit on the LCD-X, that leaves me with very little budget for an amp. I hope I'll be able to find a suitable affordable amp soon to squeeze more quality from my LCD-X.