The migration process between different third-party libraries is hard, complex and error-prone. Typically, during a library migration, developers need to find methods in the new library that are most adequate in replacing the old methods of the retired library. This process is subjective and time-consuming as developers need to fully understand the documentation of both libraries Application Programming Interfaces, and find the right matching between their methods if it exists. In this context, several studies rely on mining existing library migrations to provide developers with by-example approaches for similar scenarios. In this paper, we introduce a novel mining approach that extracts existing instances of library method replacements that are manually performed by developers for a given library migration to automatically generate migration patterns in the method level. Thereafter, our approach combines the mined method-change patterns with method-related lexical similarity to accurately detect mappings between replacing/replaced methods. We conduct a large scale empirical study to evaluate our approach on a benchmark of 57,447 open-source Java projects leading to 9 popular library migrations. Our qualitative results indicate that our approach significantly increases the accuracy of mining method-level mappings by an average accuracy of 12%, as well as increasing the number of discovered method mappings, in comparison with existing state-of-the-art studies. Finally, we provide the community with an open source mining tool along with a dataset of all mined migrations at the method level.