Synthetic lethality (SL) offers a promising approach for targeted anti-cancer therapy. Deeply understanding SL gene pair mechanisms is vital for anti-cancer drug discovery. However, current wet-lab and machine learning-based SL prediction methods lack user-friendly and quantitatively evaluable explanations. To address these problems, we propose a prompt-based pipeline for generating natural language explanations. We first construct a natural language dataset named NexLeth. This dataset is derived from New Bing through prompt-based queries and expert annotations and contains 707 instances. NexLeth enhances the understanding of SL mechanisms and it is a benchmark for evaluating SL explanation methods. For the task of natural language generation for SL explanations, we combine subgraph explanations from an SL knowledge graph (KG) with instructions to construct novel personalized prompts, so as to inject the domain knowledge into the generation process. We then leverage the prompts to fine-tune pre-trained biomedical language models on our dataset. Experimental results show that the fine-tuned model equipped with designed prompts performs better than existing biomedical language models in terms of text quality and explainability, suggesting the potential of our dataset and the fine-tuned model for generating understandable and reliable explanations of SL mechanisms.