I just received my Lyr and although I've not spent enough time with it to impart more detailed impressions (I also only have the stock tubes in place), it's clear this amp presents great bang for buck. It's solid, much smaller than anticipated and has great aesthetics.
Initial findings are that it responds very well to changes up the chain. With the upper limit of your range, you should be able to budget for a very good dac.
I agree that synergy is key with these cans. If you can put together a setup you're mostly happy with, an aftermarket cable will provide a subtle but worthwhile refinement.