This research recognizes the limitation and challenges of adapting and applying Process Mining as a powerful tool and technique in the Hypothetical Software Architecture (SA) Evaluation Framework with the features and factors of lightweightness. Process mining deals with the largescale complexity of security and performance analysis, which are the goals of SA evaluation frameworks. As a result of these conjectures, all Process Mining researches in the realm of SA are thoroughly reviewed, and nine challenges for Process Mining Adaption are recognized. Process mining is embedded in the framework and to boost the quality of the SA model for further analysis, the framework nominates architectural discovery algorithms Flower, Alpha, Integer Linear Programming (ILP), Heuristic, and Inductive and compares them vs. twelve quality criteria. Finally, the framework's testing on three case studies approves the feasibility of applying process mining to architectural evaluation. The extraction of the SA model is also done by the best model discovery algorithm, which is selected by intensive benchmarking in this research. This research presents case studies of SA in service-oriented, Pipe and Filter, and component-based styles, modeled and simulated by Hierarchical Colored Petri Net techniques based on the cases' documentation. Process mining within this framework deals with the system's log files obtained from SA simulation. Applying process mining is challenging, especially for a SA evaluation framework, as it has not been done yet. The research recognizes the problems of process mining adaption to a hypothetical lightweight SA evaluation framework and addresses these problems during the solution development.