About a year and a half ago, I tried to power the 600ohm K240 with a Corda Move. It sounded really weak and badly amplified, I was reasonably embarrassed. LISA III did worlds better next time I tried, but do yourself a favor and don't go portable with 600ohm full sized headphones.
On a side note, have noticed several movies and shows on TV that show these headphones whenever someone is in the recording studio. I know they have been professional monitoring headphones for decades, but I would not be surprised to see a spike in popularity currently.