This paper deals with the tolerance synthesis with the application for a typical Lock-or-Release (L/R) mechanism, used for Chinese Space Station Microgravity Platform (SSMP). The L/R mechanism is utilized to lock the SSMP maintaining space position during the launching stage, and to release the SSMP automatically during on-orbit stage. Manufacturing accuracy of L/R mechanism presents direct influence on its kinematic and dynamic behaviors. Tolerance synthesis can provide a reasonable assignment of tolerance, satisfying the critical assembly criteria while lowering manufacturing complexity. In this paper, based on the number-theory method (NTM), a Halton-set based Monte Carlo (MC) simulation is introduced in the accuracy model of the L/R mechanism, aiming at improving analytical precision and efficiency for tolerance synthesis. A design of experiment (DOE) based tolerance synthesis approach is proposed. With initial tolerance determined by capacity, sensitivities of different tolerance factors are generated through the first DOE stage, and then applied to determine feasible tolerance levels. The final tolerance assignments, like points scatted in high-dimensioned space with inherent uniformity, are then produced through uniform DOE in the second stage. Result shows that the majority of feasible tolerance assignments generated have more relaxed tolerance, which can facilitate the manufacturing process.