Background: Existing clinical prediction models often represent patient data using features that ignore the semantic relationships between clinical concepts. This study integrates domain-specific semantic information by mapping the SNOMED medical term hierarchy into a low-dimensional hyperbolic space using Poincar\'e embeddings, with the aim of improving lung cancer onset prediction. Methods: Using a retrospective cohort from the Optum EHR dataset, we derived a clinical knowledge graph from the SNOMED taxonomy and generated Poincar\'e embeddings via Riemannian stochastic gradient descent. These embeddings were then incorporated into two deep learning architectures, a ResNet and a Transformer model. Models were evaluated for discrimination (area under the receiver operating characteristic curve) and calibration (average absolute difference between observed and predicted probabilities) performance. Results: Incorporating pre-trained Poincar\'e embeddings resulted in modest and consistent improvements in discrimination performance compared to baseline models using randomly initialized Euclidean embeddings. ResNet models, particularly those using a 10-dimensional Poincar\'e embedding, showed enhanced calibration, whereas Transformer models maintained stable calibration across configurations. Discussion: Embedding clinical knowledge graphs into hyperbolic space and integrating these representations into deep learning models can improve lung cancer onset prediction by preserving the hierarchical structure of clinical terminologies used for prediction. This approach demonstrates a feasible method for combining data-driven feature extraction with established clinical knowledge.