Audeze highly suggests at least 1W into 50ohms. so that it can drive the heaphones without clipping. the C5 does not have enough power for that. Many people like to play the lcd2's off of cheap amps but I personally think that if you are going to buy a $1000 pair of headphones it deserves much better than a $200 amp.
This came up earlier in the thread, but I'll summarize that Audeze's power recommendations are ridiculously high. 1 watt into the LCD-2 would be over 120 dB which will melt your ears. Nobody can listen that loud without hearing damage. I believe Audeze does this on the assumption that if the amp can put out 1 watt then it will be very clean at the lower power levels people actually use. But that's not necessarily true, and if you do the math 100 mW will have plenty of headroom for any volume level that won't damage your hearing. This gives you a lot more options for a headphone amp. If you follow Audeze's 1W recommendation you'll miss out on some really clean great sounding headphone amps.
That said, the C5 is not a good choice for the LCD-2 primarily because at that price point it's simply impossible to have the quality of internal parts and design that will do justice to a headphone as transparent as the LCD-2. The C5 is also underpowered - it can only deliver about 45 mW to a 50 Ohm load. That's pitifully weak.