This paper presents the setup and results of the second edition of the BioLaySumm shared task on the Lay Summarisation of Biomedical Research Articles, hosted at the BioNLP Workshop at ACL 2024. In this task edition, we aim to build on the first edition's success by further increasing research interest in this important task and encouraging participants to explore novel approaches that will help advance the state-of-the-art. Encouragingly, we found research interest in the task to be high, with this edition of the task attracting a total of 53 participating teams, a significant increase in engagement from the previous edition. Overall, our results show that a broad range of innovative approaches were adopted by task participants, with a predictable shift towards the use of Large Language Models (LLMs).