In multi-container environments, applications oftentimes experience unexpected performance fluctuations due to undesirable interference among applications. Synchronization such as locks has been targeted as one of the reasons but still remains an uncontrolled resource while a large set of locks are still shared across applications. In this paper, we demonstrate that this lack of lock scheduling incurs significant real-world problems including performance unfairness and interference among applications. To address this problem, we propose a new synchronization design with an embedded scheduling capability, called CFL (Completely Fair Locking). CFL fairly distributes a fair amount of lock occupation time to applications considering their priorities and cgroup information. For scalability, CFL also considers the NUMA topology in the case of NUMA machines. Experimental results demonstrate that CFL significantly improves performance fairness while achieving comparable or sometimes even superior performance to state-of-the-art locks.