From the Luxman specs, it should do well.
As you can see, like most amps, each time you double the load impedance, you halve the power delivery capability of this amp, so we can see from the published spec. below, the amp will deliver 1/2 watt into 32 ohms, which means it should deliver 1/4W (250mW) into 64 ohms. The LCD-2s are 50 ohms nominally, so the amp should come close to delivering (about 340mW) into a 50 ohm load. So it should do pretty well. Just remember, the LCD-2s can handle a max input of 15 watts. 300mW should give you better than 115 dB which is way louder than you'll be able to stand.
[size=smaller] SPECIFICATIONS[/size]
[size=smaller] Continous effective output 2W+2W/8Ω[/size]
[size=smaller] 1W+1W/16Ω, [/size]
[size=smaller] 500mW+500mW/32Ω [/size]
[size=smaller] 27mW+27mW/600Ω[/size]
[size=smaller] Input Sensitivity/input Impedance unbalanced: 1.0V/26KΩ and balanced: 1.0V/67KΩ[/size]
[size=smaller] Total Harmonic Distortion 0.0025% (1KHz), 0.02% (20Hz~20KHz)[/size]
[size=smaller] Frequency Response 20Hz~20KHz (+0, - 0.1dB), 5Hz~170KHz (+0, - 3.0dB)[/size]
[size=smaller] Signal-Noise Ratio 115dB (IHF-A)[/size]
[size=smaller] Input/Outputs[/size]
[size=smaller] Input: 1 balanced pair, 1 unbalanced pair[/size]
[size=smaller] Output: 2 headphone jacks and 1 pair through RCA [/size]
[size=smaller] Power 19W[/size]
[size=smaller] Dimensions (mm) (82) W x (40) x 40[/size]
[size=smaller] Weight: (Kg) 18.3 lbs (8.3)[/size]