as the net is energy based and designed to be more invasive than harmful the armour and insulation would only be a minor obstacle. mainly cos there would be weak points at the joints where the layers would have to be thinner to allow him to move. and it works on any type of energy to varying effects, and with nothing stating otherwise it can only be assumed that the magic devise running the body is exerting energy into the body to get it to move, blocking those signals and having the same effect.

as for the lance in places where the armour is weaker for movement it won't need as much force, and like a drill it will more dig it's way through what armour there is then the pointed tip would either pierce or slip between the tube like parts you said make up the muscles with the same small blades that can 'eat' through the armour shredding them. with essentially two turns to get through that armoring before your character can move again it's not hard to believe that it's possible.

and if more time is needed lith's ability can hold you in place by essentially growing a tree on around you, turning you into part of the root system, massive strength means little if you can't move your body to use it and with the after effect of the net it would gain me a minimum of another turn to drill into him.