The advent of 5G and its ever increasing stringent requirements for bandwidth, latency, and quality of service pushes the boundaries of what is feasible with legacy Mobile Network Operators' technologies. Network Function Virtualization (NFV) is one promising attempt at solving some of those challenges that were widely adopted by the industry and the standardization bodies. At its essence, NFV is about running network functions as software workloads on commodity hardware to optimize deployment costs and simplify the life-cycle management of network functions. However, it introduces new fault management challenges including dynamic topology, multi-tenant fault isolation and data consistency and ambiguity; that we propose to define in this paper. To tackle those challenges, we extend the classical fault management process to the virtualized functions by introducing LUMEN: a Global Fault Management Framework. Our approach aims at providing the availability and reliability of the virtualized 5G end-to-end service chain. LUMEN includes the canonical steps of the fault management process and proposes a monitoring solution for all types of Network virtualiza-tion Environments. Our framework is based on open source solutions and could easily be integrated with other existing autonomic management models.