There can never be consensus on this topic. Some people won't consider tubes; others won't consider solid state. Some can;t spend more than $500; for others, money is no object. Even given just those two factors, before we ever discuss actual synergy with the LCD-2, you have no chance at consensus.
For me, the ideal amp for the LCD-2 is the Decware Mini-Torii. Lots of power, sounds great, not horribly expensive. The downsides are that it really isn't good for using with other types of headphones, just other planars like the HE-6, and that while it's worth the money IMO, it's still $1,500.
I actually prefer the Leben CS300X with the LCD-2, but at the current US price of $3,800, it's getting really hard to recommend, given how good the Decware is at $1,500.
I really like your view on it, would you say the Cavalli Audio Liquid Fire fits in between the two with price/performance levels?