Favorite amps for the K1K are foo_me's zanden amp and voltron's Moth Audio 300B amps. Neither are going to be as good as is possible since both aren't impedance matched nor designed specifically for the K1K. If you use resistors to better match impedance (Which wasn't done when I had heard either with the amps) performance theoretically should improve. Better can be done, but probably requires a custom design from someone with some serious chops and some familiarity with the headphone. deepak has heard them through his friend's custom amp with lundahl iron and interesting high performance tubes (Not your usual 6sn7 driving 300b shlock) that probalby is up there as well, but I haven't heard it.
I'd say for about 5-10k in parts you can create the ideal k1k amp depending on how pricey you want to go with iron/chassis and how rare and esoteric you want to go with tubes. You could probably do a fricken great job with 1-2k in parts non including chassis/tubes. Neither option makes sense for me at this time though it would if I had high efficiency speakers of similar impedance that I could drive with the same amp, but I don't.
As far as LCD-2. Well I think my balancing act and solid state are both pretty good. The balancing act is transformer coupled and will do good with anything down to 32 ohms. The solid state performs well with any load. But none of this stuff is the BEST BEST out there for anything. The dynafet and a few other solid state diy projects edge out barely my dynamid and dynahi... and there are better diy tube amp designs out there than the balancing act that I've heard about. Better in a theoretical standpoint not an observed standpoint. And also you can take fancier designs and chose parts that better match the LCD-2. I could have my amps that I own now tweaked in that manner, but I won't.
I'd say what I have and how commercially available it is I'd say what I have is about as good as it gets. TTVJ 307A is good. ZDT is good. Beta22 is pretty good. That moon audio lundahl iron amp is probably pretty good. GS-X which basically is what my balanced reference is pretty good. That's about all that I'd even look at from commercial makers. There are some exceptions where some speaker/audio company makes a 1 off, but those things always seem overpriced to me because you pay for the 1 offness. You don't get the bulk parts price breaks trickled down to you. Still, expensive as they are some of them are great. For anything better and of better value you are going to have to make friends with a skilled DIYer/Designer and then mooch free labor and find someone that is good at sourcing unobtanium transistors, passive parts and tubes.
