Do you think an amp at any price would really make a noticeable difference? At this point, I feel like we're fighting for extremely minuscule improvements.
Definitely quality amp with quality power supply will make improvement, I think O2DAC with nice quality amp as I wrote would be great system to start. And you can try some nice silver or cooper heaphone cable for your LCDX in future too.
But you bought nice system O2+ODAC, LCDX is easy to drive so it needs system with neutral tones or a little more brighter character will be fine too..