The emergence of Self-Driving Laboratories (SDLs) transforms scientific discovery methodology by integrating AI with robotic automation to create closed-loop experimental systems capable of autonomous hypothesis generation, experimentation, and analysis. While promising to compress research timelines from years to weeks, their deployment introduces unprecedented safety challenges differing from traditional laboratories or purely digital AI. This paper presents Safe-SDL, a comprehensive framework for establishing robust safety boundaries and control mechanisms in AI-driven autonomous laboratories. We identify and analyze the critical ``Syntax-to-Safety Gap'' -- the disconnect between AI-generated syntactically correct commands and their physical safety implications -- as the central challenge in SDL deployment. Our framework addresses this gap through three synergistic components: (1) formally defined Operational Design Domains (ODDs) that constrain system behavior within mathematically verified boundaries, (2) Control Barrier Functions (CBFs) that provide real-time safety guarantees through continuous state-space monitoring, and (3) a novel Transactional Safety Protocol (CRUTD) that ensures atomic consistency between digital planning and physical execution. We ground our theoretical contributions through analysis of existing implementations including UniLabOS and the Osprey architecture, demonstrating how these systems instantiate key safety principles. Evaluation against the LabSafety Bench reveals that current foundation models exhibit significant safety failures, demonstrating that architectural safety mechanisms are essential rather than optional. Our framework provides both theoretical foundations and practical implementation guidance for safe deployment of autonomous scientific systems, establishing the groundwork for responsible acceleration of AI-driven discovery.