Great sounding headphone systems are built around great high powered electronics built for driving headphones. Also, the investment is much like that in a main system. Think 5 to 10 times more on electronics than on the headphones.
I have had high end headphone system of fifty years... upgrading with the availability of equipment. I can say my current system far exceeds anything I thought was possible only a few years ago. And it requires massive power to get the most out of every set of headphones (see my Virtual Systems for my headphone system).
Look to Woo for headphones amps. Virtually all are tubed and are incredibly good. I have the WA5, which can be used to power speakers. It completely takes charge of all of my flagship headphones... like Sennheiser, Focas, Ultrasond, Dennon... etc. They all start sounding much more similar because of the incredible power and natural nature of the amp.
If you want a great sounding headphone system... concentrate on getting a great / powerful headphone amp. The Lyr3 is not it.

