Hey all, picture for fun before i answer some questions.
First, I had the k702 a long time ago, like years... in head-fi that is forever and my memory of them was a much more sterile sound than the q. I cant really compare them though since i didnt have a lyr back then... All i had was a trashy indeed hybrid off ebay :p For headroom to post different graphs that sort of confirm what we all hear between the 70x series i think there is a significant difference in sonic characteristic between the k70x and the q701.
Second, the Lyr does a killer job of driving the q. The dynamics and oomph from it are amazing for the q. I have heard a q from a nuforce hdp and it too had enough power for the q and surprisingly wasnt too bright which i thought was wierd since the hdp is considered a tad bright. The Lyr is like smelling a boquet of roses while the headphone jack on my computer is like smelling a boquet of dandelions. You still have a boquet of flowers but obviously the roses smell way better :-) There is no way you could go wrong with the lyr and a q IMO. If I were you and getting a Lyr I would get it with the 6n1p tubes from schiit ($20). I have them and they are second best behind the Lorenz I love. I am considering the CTH hybrid to save on some cash but retain the quality. LFF who built my paradox likes the CTH better (more 3d) than the Lyr with the paradox and i would assume they drive the q701 just as well since many people state the cth drives akg's well.
Third, Although I never had all the amps at the same time ( Asgard, Valhalla, M-stage, Lyr) at the same time I am confident in saying it is better. It is so dynamic and clear. It's sort of like comparing apples and oranges though since they are all different types of amplification. Hybrid (Lyr) Solid State (Asgard,M-stage) Tube (Valhalla). I did prefer the M-stage over the Asgard but that was mainly becasue it was a warmer feel and it went well with my headphones at the time. The Asgard did not drive my k601 well at all but the hd600, that was an amazing match!. The Lyr has a great amount of tight solid state feel with a perfect amount of tubey goodness mixed in which is great for the q701 which could use a bit of smoothness and extra oomph. For me the Asgard was nothing special, the M-stage was a bargain but I wanted to take the next step and went to the Lyr and the Valhalla was an experiment with tubes and went back within 15 days because it just didnt wow me but dam it was pretty.
Fourth, As for the 880's 600ohm. they were very good and I think I still regret unloading them a bit. They were too much like my paradox, "flat", but didn't have the intimate vocals the paradox did which I really love. The q701 is a definite more fun listen for me.
Hope this answered most of your questions.
As a parting plug for music for the q701, check out "The Arrival" by thePhantom on his Release album. It is flippn sweet on the Q!
Link--- http://music.phantastic.me/album/release Check out some of his stuff. The fountain of youth album is pretty good too! Free downloads!