An example of how i print a lithothane veritcally. Included image is sourced from:
Original lithothane was at https://makerworld.com/en/models/31881#profileId-128807
I regenerated the lithothane and made a vertical orientation with the print settings i use when printing one of these.

I usually print at .04 layer height with a .2 nozzle but since i know it's rare to have one of those installed, these simple print settings work great, while it may be slightly slower than printing in the horizontal plane, using vertical with a .08 layer height and Arachne slicing, as well as running slower accelerations will allow you to achieve amazing resolution in your lithothanes.