I agree the LCD-2 doesn't need nearly as much power as Audeze recommends - their recommendation of 1 watt is at least 10 times higher than you really need.
The LCD-2 needs about 0.2 mW for 90 dB SPL (which is very loud).
1 Watt is 5,000 times more power. That's 37 dB louder, which is 127 dB SPL, which will fry your ears & melt your brain.
Even a measly 100 mW is enough for an LCD-2, if the amp produces that 100 mW cleanly and effortlessly. That 100 mW makes 117 dB SPL, which is loud enough to cause hearing damage with less than 1 minute of exposure. Anyone who listens that loud would soon lose his hearing.
The LCD-2 is an efficient, purely resistive load that is easy to drive, and 70 ohms isn't too low an impedance for any solid state amp. Tube amps will need an output transformer - an OTL tube amp won't drive a 70 ohm load well.
The amp driving LCD-2 doesn't need a lot of power. It just needs to be clean, very clean. Audeze's recommendation stems in part from the fact that a powerful amp loafing along at less than 1% of its rated power is probably clean. That's often true, but not always. Most of the time, a cleaner amp will sound better than a more powerful one.