Selecting appropriate libraries is important when generating code, especially when the library evolves rapidly, e.g., libraries can be obsolete because of deprecated, vulnerable, and the emergence of better alternatives, and need to be updated in the repository. While large language models have shown impressive capabilities in library selection when generating the code, recent studies have not explored library selection when generating code that can also be implemented by obsolete libraries. To fill the gap, we explore whether LLMs can use appropriate libraries in the generated code when answering the Stack Overflow questions that were originally answered with obsolete libraries. We extract 20 obsolete libraries from the library migration history and 667 related Stack Overflow questions. Our results reveal that LLMs struggle with certain obsolete libraries undergoing security-driven and alternative-driven due to challenges such as serialization risks and the absence of well-documented migration paths, as well as data processing libraries involving complex format changes. In contrast, they perform well with long-unmaintained libraries and those related to Web and system utilities. Furthermore, questions explicitly mentioning obsolete libraries would instruct the LLM to directly generate the code with obsolete libraries rather than recommending up-to-date libraries. To improve the performance of LLM in selecting appropriate libraries, we explore different prompt refinement strategies, including explicitly showing deprecated libraries and suggesting up-to-date alternatives. Our findings show that refined prompts significantly enhance the ability of LLM to select appropriate libraries, offering valuable insights for optimizing LLM-driven code generation in evolving software ecosystems.