Military logistics is a complex process where response times, demand uncertainty, high variety of material references and cost effectiveness turn decisive for combat capability. Considered as the bridge between the deployed forces and the industrial base that provides materials and services that the forces needed to accomplish their mission, capacity and efficiency of delivery are required for its processes. The required flexibility could only be achieved by improving the Supply Chain Management (SCM) in order to optimize delivery lead times. To cope with these requirements, lean thinking can be extended to military organizations. This research justifies and proposes the use of Lean Six Sigma (LSS) methodologies from manufacturing to optimize logistics processes in the defense sector. In particular, the article presents the benefits and results obtained using Value Stream Analysis and DMAIC (Define, Measure, Analyze, Improve, Control) problem-solving methodology to improve the order processing lead-time as key performance indicator of a military unit delivery fulfilment.