The primary effect of balanced is more power. More power with the Audeze headphones results in more dynamic range. The lyr has more than enough power already so for you power is not a requirement from balanced output.
This is from Audeze regarding amp requirements for the LCD-2:
"When deciding what amp to buy It is very subjective and opinions vary a lot. Here are some thoughts on selecting a good amplifiers
for LCD-2. We have tested the LCD-2 with quite a number of studios and recording engineers.
The LCD-2 has an impedance of 50 ohms, which is purely resistive and is almost perfectly flat across the entire frequency range.http://www.audeze.com/2009/12/waterfall-plots-low-frequency-extensi...
Lets us say you listen to symphony-orchestra. This type of music can have dynamic range of 60 dB. i.e if silence (room noise) is at 60 dB (LCD-2 is pen type headphone design with almost no attenuation of ambient noise) and the maximum occasional peak needs to be 120 dB. I am just giving an example here, but depending upon the type of music and the recording this varies. 120 dB is very loud - almost Rock Concert level close to the speaker.
For the LCD-2, if you put 1 mw of power, you get about 90dB output. For this example, let us assume 90dB is the level you listen normally. To reproduce the occasional 120 dB peak without clipping on the LCD-2, the amplifier would have to output 1000 times more power than 1mw, i.e 1 W.
So, an amplifier that can output 1w is the bare minimum. Amplifiers will have distortion metrics at different wattage levels. If an amp can output maximum 1w it would be barely sufficient and might have a lot of distortion at full output.
So I would suggest an Amp that would at least be able to provide a couple of watts of output without any clipping. Damping in amplifiers is not a big problem for LCD-2 since the impedance doesn't vary."
For noise rejection it helps with the clarity of the signal which helps the sense of imaging and placement of instruments and sense of soundstage. The difference from SE to balanced can be subtle in this regard though, however I enjoy it over single ended. When volume matched the differences between balanced and SE output aren't as large as one may think if there is enough power in both applications.