Distributed -mutual exclusion ensures that at most a single process has permission to access each of the copies of a critical resource. In this work we present an autonomic solution for distributed -mutual exclusion that adapts itself after system changes. Our solution employs a hierarchical best-effort broadcast algorithm to propagate messages reliably and efficiently. The broadcast is based on another autonomic building block: a distributed algorithm for creating and maintaining spanning trees constructed in a fully distributed and adaptive way on top of a virtual hypercube-like topology, called VCube. The proposed solutions are autonomic in the sense that they reconfigure themselves automatically after the detection of faults given the set of correct processes in the system. All proposed algorithms are described, specified, and proofs of correctness are given. Results from simulation show that the proposed approach is more efficient and scalable compared to other solutions.