Well, I'm no expert, but this is my comment.
The leathern lestovka reflected Eastern monastic practice in terms of a symbol reminding one that we should be "dead" to the world and thus leather is the hide of a dead animal (this also applies to the leather monastic belt etc.).
The lestovka is a Russian development that had nothing to do with the Greek Komvoschinion in terms of opposing it and the like. The Lestovka is a form of the Chotki of St Basil the Great, except that it reorganizes the one hundred parts in a way that provides a reflection on Christian truths. Thus, the nine major steps or dividers refer to the nine Choirs of Angels, the first twelve minor steps - to the Apostles, the next 38 to the weeks and two days Christ was in the Womb of His Mother, the next 33 to the years of His earthly Life, the next 17 to the prophets, with the spaces at either end symbolizing heaven and earth, the stitching the teaching of Christ, the four sides of the triangular endings, the four Gospels and the triangular shape the Holy Trinity. There is also a seven moveable piece attached to the "leaves" of the lestovka to help one count the seven times it should be said, at a minimum, daily in honour of the seven Mysteries etc. (Although I've yet to find such on any leather lestovka I've ever owned.)
It became popular after Nikon and Russian Saints like St Seraphim of Sarov used a Lestovka (which led one Russian writer to comment that Old Rite practices continued in many Russian monasteries even after Nikon's reforms).