Accurate prediction of synthetic lethality (SL) is important for guiding the development of cancer drugs and therapies. SL prediction faces significant challenges in the effective fusion of heterogeneous multi-source data. Existing multimodal methods often suffer from "modality laziness" due to disparate convergence speeds, which hinders the exploitation of complementary information. This is also one reason why most existing SL prediction models cannot perform well on both pan-cancer and single-cancer SL pair prediction. In this study, we propose SynLeaF, a dual-stage multimodal fusion framework for SL prediction across pan- and single-cancer contexts. The framework employs a VAE-based cross-encoder with a product of experts mechanism to fuse four omics data types (gene expression, mutation, methylation, and CNV), while simultaneously utilizing a relational graph convolutional network to capture structured gene representations from biomedical knowledge graphs. To mitigate modality laziness, SynLeaF introduces a dual-stage training mechanism employing featurelevel knowledge distillation with adaptive uni-modal teacher and ensemble strategies. In extensive experiments across eight specific cancer types and a pancancer dataset, SynLeaF achieves superior performance in 17 out of 19 scenarios. Ablation studies and gradient analyses further validate the critical contributions of the proposed fusion and distillation mechanisms to model robustness and generalization. To facilitate community use, a web server is available at https://synleaf.bioinformatics-lilab.cn.