I have Lcd2 fazor edition, it's easy to drive, and Sony zx300. They sound great together via single ended output. Balanced output is more powerful and I think it would sound very well with LCD2c but as you say, not at full potential.
I would say either buy LCD2 fazor or if you want LCD2c, you might try a topping dac/amp or an ifi micro idsd, or if you add some money, the black label edition of ifi micro. They sound great together, still not at the full potential but you kind of need to double or triple the budget for a dac/amp to reach the potential these headphones have. Try to find used devices, on my country I've seen ifi micro bl sold for around 220 euros.