Computational synthetic lethality (SL) method has become a promising strategy to identify SL gene pairs for targeted cancer therapy and cancer medicine development. Feature representation for integrating various biological networks is crutial to improve the identification performance. However, previous feature representation, such as matrix factorization and graph neural network, projects gene features onto latent variables by keeping a specific geometric metric. There is a lack of models of gene representational latent space with considerating multiple dimentionalities correlation and preserving latent geometric structures in both sample and feature spaces. Therefore, we propose a novel method to model gene Latent Space using matrix Tri-Factorization (LSTF) to obtain gene representation with embedding variables resulting from the potential interpretation of synthetic lethality. Meanwhile, manifold subspace regularization is applied to the tri-factorization to capture the geometrical manifold structure in the latent space with gene PPI functional and GO semantic embeddings. Then, SL gene pairs are identified by the reconstruction of the associations with gene representations in the latent space. The experimental results illustrate that LSTF is superior to other state-of-the-art methods. Case study demonstrate the effectiveness of the predicted SL associations.