I do not disagree with your opinion, we all hear different. But as an owner of both amps, my ears, not my mind prefers the Lyr with some premium tubes over the 337 with premium tubes with the HE500. Granted I have spent a ton of money finding the perfect tubes to my ears (it is an addiction no doubt) to find what I have now, but I am actually down to three sets ATM for the Lyr after trying well over 150 sets. The Lyr is not the best amp I have heard/own, but at its price point and some research on tubes it has very good synergy with the HE500.
My DAC upgrade was the biggest change in sound to my ears.