Although I've auditioned both the LCD 2 and the Lyr 2, I do not own them, so take what I say with that grain of salt. I have not heard the Deckard.
Mjolnir's big benefit over Lyr is balanced operation. If you like balanced, or think you will like balanced, buy it with confidence. If you don't anticipate going forward with that, Lyr's single ended is more powerful than Mjolnir's single-ended, though I can't say for certain whether it's better on all counts. Mjolnir 2 has a noticeably more neutral, linear sound through balanced. I noted a degree of smear in Lyr by comparison. If you like tubes, MJ2 will do excellent things with them, but to realize its full potential, again, you do need balanced operation.
I would recommend the iFi tubes for Audeze—they're perhaps the best overall fit for the amp. My '68 orange globes would probably just suffocate you in the warm sound (though they work great with HD800 or K1000).