Not quite. The Soloist does not do a very good job with my HE-6 (which is understandable), HD800, and even TH900 (which is said to be an easy headphone to drive). It is okay with HD650 and LCD-3 though, and although I don't own it anymore, the HE-500 was a good match with the Soloist. At any rate, I wouldn't call the Soloist a great all-rounder amp... but I do think it might work out well with LCD-X.
As for the SPL Phonitor, I wouldn't use it to drive anything other than HD800. It is okay on the HD800, but bad with pretty much everything else.