It does indeed. My previous fave cable with the LX before I went nuts and got a Cardas.PW No. 10 works well on my LX and is very reasonable. Build quality is top notch and there is no microphonics and not stiff.
Shameless plug, my No. 10 is up for grabs. Negotiable. https://www.head-fi.org/classifieds/pw-audio-anniversary-no-10-8-wire-cable-2-pin-4-4mm-mint.5066/