I always thought LCD-2s were closed but Tyll Hertsens lists their measurements in the circumaural open category. And having taken his pair apart, he ought to know. Go figure.
These orthos are doing pretty well in measurements actually, particularly low-frequency distortion (regardless of whether it's the LCD-2 or one of the Hifiman units). Conventional open cans can't touch them in that regard. Their impedance response is pretty much ruler-flat, too. They are, however, quite inefficient. LCD-2s already are the least critical of the bunch, so I'd trust even a rather inexpensive amp like the FiiO E9 to drive them fairly well. Still, any old Cmoy can drive a HD800.