Container-based microservice provisioning, with its elasticity in terms of the layered structure, enables the sharing of common layers among different edge computing tasks, both within and across edge servers (ES). However, due to the potential hardware breakdowns, each ES may prone to failures, affecting its lifetime (i.e., the time-length that an ES works continuously without interruptions), and in turn leading to the collapse of their hosted/provided microservices or the other ESs’ microservices requesting common layers from it. Obviously, if such an issue cannot be well addressed, the reliability of microservices in serving corresponding tasks may be severely reduced. In this paper, we study the microservice deployment optimization with layer sharing for maximizing the system-wide reliability while satisfying all tasks’ delay requirements. Considering dynamic task generations and the asynchronization of various decision variables with different triggers, we design an online optimization algorithm by leveraging an improved Lyapunov technique integrating randomized rounding and Lagrangian method, which iteratively solves the problem over different timescales. Theoretical analyses and simulations evaluate the performance of the proposed solution, and show its superiority over counterparts.