The Lyr may drive the HE-6 but does not define nearly its potential. It's a night and day headphone when hooked up to a Mjolnir IMO in terms of the low end and the clarity/sound stage it opens. My LCD-2 is on the way (going to be used for a transportable rig) so I can't comment on that, but from what I've heard on the LCD-3 and how people describe the differences, I think you'll be very happy with the LCD-2 in combination with the Lyr. However, I want to throw a wrench in there.....and that's the HE-500 pairing with the Lyr. IMO this combination really has great synergy and it's my go to headphone with the Lyr out of my assortment. The remaining I prefer on the Mjolnir most the times unless I'm listening to some vocals that I prefer the "tube" sounds with.....the HD800 these days I don't prefer all that much.....as I mentioned before, too brutal and revealing and fatigues the listener without engaging them with the warmth/low end LCD-3/HE-500/HE-6 does. I bet these HD800 would work great in a studio when you're trying to be analytical all day....but it doesn't give me much enjoyment. IMO Iamnothim you should really be looking at the HE-500 or the LCD-2 for the Lyr.
Would you say that the HE-500 sounds better than the HE-6 on the Lyr?