Generating lay summaries of biomedical research remains a time-intensive task, despite their importance in bridging the gap between scientific findings and non-expert audiences. This study introduces a retrieval-augmented fine-tuning framework for biomedical lay summarization, integrating abstract-driven semantic retrieval with LoRA-tuned LLaMA 3.1 models. Abstracts are used as queries to retrieve relevant text segments from full-text articles, which are then incorporated into prompts for supervised fine-tuning. Evaluations on the PLOS and eLife datasets show that this hybrid approach significantly improves relevance and factuality metrics compared to both base models and those tuned individually, while maintaining competitive readability. Prompt design experiments highlight a trade-off between readability and factual accuracy. Our fine-tuned model demonstrates strong performance in relevance and factuality among open-source systems and rivals closed-source models such as GPT, providing an efficient and effective solution for domain-specific lay summarization.