Hi Slavkok;
if you want to eliminate backlass in the lead screw nut try this;
machine 2 nuts about 20 long each
in the face of the nuts ,drill and ream 2 off 2mm holes that
are exactly on the same position than the other nut (you can use part of the lead screw to align it.
now fit a 2mm x 50 long steel dowel thru both holes in both nuts , fit a spring outside the diameter exposed in both dowels , effectively pushing both nuts away from each other , that will get rid of your problem
regards
mariano