All those headphones are lower impedance and all those amplifiers are Output Transformerless amplifiers. OTL amps have a lot of voltage but their power delivery is flipped over due to low current performance - they make a lot of power at 300ohms for not a lot of money and size due to the absence of the output transformers but they make the least amount of power at 32ohms. You'll distort if not also clip a lot sooner, on top of which the output impedance is a lot higher (even the Valhalla2 is only low for an OTL) and it is not easy to predict without all the relevant data whether your headphones will sound like tin cans like the K701 on the Little Dot MkII or do the opposite and sound like a mudslide with flabby and uncontrolled bass hits. Basically even the Valhalla2 is best used with high impedance reference headphones and then it happens to be less unpredictable in case you use lower impedance headphones for casual listening, particularly if you have ones that have a high enough sensitivity so lower power isn't a problem (note that even Grados can sound like tin cans on some amps that have high output impedance).
Given your most likely reference headphone in that set is the LCD-X you might as well get a decent hybrid amp or if you can afford it, a transformer-coupled tube amp, unless you plan on getting an HD800S.
Given your headphones, yes. And whatever you upgrade to later on will work well on it anyway - high impedance headphones have high sensitivity anyway so even if you get an HD800 they won't have any problem on conventional power delivery that drops at high impedance barring some circuits that really drop the output.
