The adoption of Open Source Software (OSS) by organizations has become a strategic need in a wide variety of software applications and platforms. Open Source has changed the way organizations develop, acquire, use, and commercialize software. Further, OSS projects often incorporate similar principles and practices as Agile and Lean software development projects. Contrary to traditional organizations, the environment in which these projects function has an impact on process-related elements like the flow of work and value definition. Process metrics are typically employed during Agile Software Engineering projects as a means of providing meaningful feedback. Investigating these metrics to see if OSS projects and communities can utilize them in a beneficial way thus becomes an interesting research topic. In that context, this exploratory research investigates whether well-established Agile and Lean software engineering metrics provide useful feedback about OSS projects. This knowledge will assist in educating the Open Source community about the applications of Agile Software Engineering and its variations in Open Source projects. Each of the Open Source projects included in this analysis has a substantial development team that maintains a mature, well-established codebase with process flow information. These OSS projects listed on GitHub are investigated by applying process flow metrics. The methodology used to collect these metrics and relevant findings are discussed in this thesis. This study also compares the results to distinctive Open Source project characteristics as part of the analysis. In this exploratory research best-fit versions of published Agile and Lean software process metrics are applied to OSS, and following these explorations, specific questions are further addressed using the data collected. This research's original contribution is to determine whether Agile and Lean process metrics are helpful in OSS, as well as the opportunities and obstacles that may arise when applying Agile and Lean principles to OSS.