The Sex is the non-OTL version of the Crack (different circuit but voiced with similar goals) which is suited for high Z headphones. The Sex is designed to push power into low Z headphones. Alternatively you can add a choke to the Crack and be able to run low Z headphones properly but how much it changes the sound compared with it I can't say.
The only tube amp I can recommend for the LCD2's or any power hungry headphone is the LD MK VI+ with the appropriate tubes this amp destroys every Woo I've had a play with up to the WA5 levels but yet again Jack Woo prefers aesthetics and quality over circuit implementations and that's where most of his high rise price charges are from.
Given that I've built a few B22 and M3 amps both balanced, active and passive ground configurations, the M3 is almost a B22 except a few things, it is OPAMP based and as fishski has mentioned with the appropriate mA tuned with bigger sinks for heat dissipitation, power output levels can be matched to the B22, but a B22 can be pushed for more to suit what ever heavy duty load you will be powering it for.
I would describe the M3 as a warm sounding version of the B22, the B22 complements the Audeze orthos very well (bright or flat sounding amp meets laid back warm darkness), the same as the Mjonir. I haven't heard the Bryston BHA-1 but it is often described as too clinical or bright sounding with the HD800's from other users so it may be a good match with the LCD2's.
I really liked the Violectric V100/V200/V181 series amplifiers when I heard few years back with the rev.2's when it came out (enjoyed it with the HD580/600/650's as well). The V100 is pretty much 80-90% of the V200 while costing $200-300 cheaper. I could not discern much differences between the V181 and V200 in SE mode but balanced out the soundstage is incremented by a subtle bit, subjectively enough for some to state it is a whole lot better but not the case IME.
From what I've gathered the V181 is a balanced version of the V100 which I use to think it a balanced V200 due to hardly any differences in sound between the V200 SE out and the V181 SE out, but I was corrected on this. Opamp also has no affect on the Violectrics and is a good way to void your warranty. Avoid any of the Violectrics with the rev.1 LCD2's as it get's too romantic and mushy sounding.
Although I'm not a fond fan of the Burson line of amps, the only decent sounding (but far perfect matching) amp with the LCD2's is the Soloist/Conductor (same thing just with a DAC). Detail retrieval is not the biggest point of the Soloist but it is a good sounding, what I don't like may be something you may.
And finally, if you have $600-800 to drop on a new or used Schiit Mjonir, I recommend doing so. I've been a bit wary of Schiits past amps due to the incident of some of there amps killing headphones with no DC relay implemented, the Mjonir is almost the perfect amp for the LCD2's rev.1 or rev.2 if you can dismiss the fact that you'll have to run balanced (so extra cost, but imho very worth it if you're after a bit of refinement).
Powering the orthos off speaker amp's/vintage amplifiers is a another whole story.
