For what its worth, I have my LCD 2.2 hooked up to the Lyr and alternate the amp with the Burson Soloist. Fantastic amps both with plenty of headroom for the LCDs. The Mjolinir is a balanced amp and unfortunately I have had no experience with balanced anything. That will change soon, though.
When do you reach for the Lyr instead of the Soloist (for use with the LCD-2)? What traits does the Lyr offer that the Soloist lacks?