The SEX amp is a much, much better choice for the LCD-2. A Crack will have issues with both the output impedance and the cutoff frequency of the coupling caps at the output with a 60 Ohm headphone, and the low sensitivity will not help either.
Everyone should have a Sex amp or two around. Headphone amps, speaker amps, line stages with uber low output impedance and no cathode follower, you name it.