This snake was made by Bev Walker; it too spirals quite a lot, again in the S direction. It was made with Zwicky Ursus 50 passives and Valdani 50/3 workers; both Z-spun threads.
This phenomenon seems to occur most markedly in half stitch and to a lesser extent in fairly open stitch combinations; presumably because the threads of the lace are able to move slightly. In laces with a lot of extra twists and/or the texture is very close there is less opportunity for the threads to move. One of the snake samples I worked, using Tootal Sylko which is Z-spun, was a practice Milanese braid "Figure of Eight" chosen because it has a large number extra twists to unbalance the Z-spin. It lays flat! I can only think that that is because all the twists hold the threads firmly in place and are unable to move.
So which threads are Z-spun and which are S-spun? Generally, anything which is designed primarily for machine stitching will be Z-spun whilst most cotton threads intended for hand embroidery are S-spun. Linen is nearly always S-spun (I read somewhere that this is because linen bast fibres have a natural tendency to spiral in the S direction anyway). Weaving threads may be spun in either direction and most crochet/tatting threads are double spun, ie three S-spun threads doubled in the Z-direction making a 2S-3Z thread (which does torque). Many glitter threads are of a chain or woven construction and some are metalised polyester wrapped around a filament fibre core which is not the same as spinning. The sample snake I made using a wrapped glitter thread is very stiff but lies flat.
Another sample which curls is made with Multistrand Inox from Bart & Francis. This is a thread made from very fine strands of stainless steel loosely spun together in the Z direction to make a singles thread. The lace is balanced in that it is mostly cloth stitch, CTC, but the thread is still trying to compensate for its Z twisted structure and the lace is curling in the S direction.
NB: the direction of spin I refer to here is the final direction of plied/folded threads.