We consider an uncapacitated multi-echelon lot-sizing problem within a remanufacturing system involving three production echelons: disassembly, refurbishing and reassembly. We seek to plan the production activities on this system over a multi-period horizon. We assume a stochastic environment, in which the input data of the optimization problem are subject to uncertainty. We consider a multi-stage stochastic integer programming approach relying on scenario trees to represent the uncertain information structure and propose a solution method based on an extension of the stochastic dual dynamic programming algorithm. Our results show that this approach can provide good quality solutions for large-size instances in a reasonable time and significantly outperforms the use of a stand-alone mathematical solver.