The Mullards are dutch right? Same with the Siemens CCA? Those are both warm right? Well I am kinda hoping that the sound-signature changes with the HD800S. I switched my Shure SRH1840's for my older Beyerdynamic 990 pro's and the soundsignature did improve (much warmer and much more bass).
It might be not completely the default stock tubes their fault. Maybe it is just the Shure's SRH1840's (64 ohm) that doesn't pair well with the Lyr-2.
I mean the BeyerDynamics 990 pro's (250 ohm) do sound better on either low or high gain-setting.
Saving money on a set of cans is not a option. I will regret that. I'll go for the Sennheiser's. Then the month after other tubes together with a DHC compliment4 cable.
I remember the stock tube as not especially exciting, but not that variable and outright bad. Don't think it's the low impedance of the 1840s either, that should not be a problem with the Lyr2.
You can double check the signal and power feed, might be something contaminating one of them and then being amplified. If you eliminate that then you know the problem is with the tube/amp/dac.
Power direct from the wall is always a good check, away from other equipment and wire.
If you are looking forward to the HD800s, this might be useful: read rb2013's 6922 Tube Review thread, or this shorcut post summary (post #342):
He used the Lyr1 and the HD800 (not the 800S).
http://www.head-fi.org/t/761078/6922-tube-review-17-top-6922-6n23p-e88cc-cca-7308-e188cc-tubes/330#post_12651200
The Black Dragons were part his solution to tame the highs of the HD800. You might not find any issue there with the HD800S. But important to note that he was using a different DAC.
I have the Lyr1 and 2, fed by the Gumby. I find all/most of the usual suspect tubes to be good with this combination, if it's a good pair of tubes. (Have not tried Mullards.) However I do have my own favorites, not exactly aligned with these choices.
(Don't have the time right now to list my favorites.) Thought the link might be at least one good summary perspective for the HD800S.