Knitted lace stockings in fine wool look rather good, though I don't know where they could be bought.

A small vertical pattern, repeated several times with narrow bands of rib in between, or an all over pattern with a narrow stocking stitch panel centre back in which to do the increases work well.

You need the centre back panel in all over lace otherwise it gets really confusing as to where you are in the pattern - unless you like living dangerously.

I think they could be done on a knitting machine - though I have not tried it. I do lace, and I have knitted socks but not at the same time.