I can state from my experience with various headphone amps and a variety of LCD (LCD-2f ,X and 3f) headphones, they benefit greatly from fast amps. That usually means solid state. And for me, I narrowed it down to Burson.
I happen to believe that the synergy between Burson Amps and Lcds is fantastic. Bursons have the heft and sparkle that really brings the Lcds to life. I recently violated my own advice and bought a Schiit Mjolnir 2 with some of the best known tubes for it amongst other tubes. I used it in balanced mode. I tried se mode, and it was just sad , sound quality wise and lacked power too. After two weeks of giving it a chance, I decided to reconnect my Burson Soloist.
It was an AHHHH moment. Life returned to the music. The weight of the bass was back. Tight and controlled.That Burson sparkle to the high end (not brightwise) was back. Needless to say, I sold the Schiit.