The BHA-1 is an extremely balanced amplifier and it's power delivery is quite linear meaning all the frequencies are amplifierd equally so even at full volume, the sound is very consistent. In that respect, it will work excellent with any headphones you might wish to use with it as long as the impedance of those headphones is sufficiently high.
If HD800 and LCD2 cost the same, then you have to decide for yourself. I will tell you this though - the transient response (the attack and drama) as well as detail resolution and spatial imaging is way better on HD800 than even the LCD3. If that is something you like, then HD800 is your candidate. If you like more pace and added extension in the low end as well as withdrawn top end, then LCD2 will be more to your liking, especially because it will be more forgiving with average recordings.
The HD800 is built to a much higher standatd than the LCD2 and LCD3. The point in fact is, the materials used for HD800 are composite and believe me, I know something about these. They will last. I have not heard any complaints regarding the Sennheiser, especially the HD800, whereas I have heard criticisms about Audeze's quality more than once.
Hope this helps!
Post a picture when you make a decision and buy something!
Cheers!
Antun