Despite the growing use of Electronic Health Records (EHR) for AI-assisted diagnosis prediction, most data-driven models struggle to incorporate clinically meaningful medical knowledge. They often rely on limited ontologies, lacking structured reasoning capabilities and comprehensive coverage. This raises an important research question: Will medical knowledge improve predictive models to support stepwise clinical reasoning as performed by human doctors? To address this problem, we propose DuaLK, a dual-expertise framework that combines two complementary sources of information. For external knowledge, we construct a Diagnosis Knowledge Graph (KG) that encodes both hierarchical and semantic relations enriched by large language models (LLM). To align with patient data, we further introduce a lab-informed proxy task that guides the model to follow a clinically consistent, stepwise reasoning process based on lab test signals. Experimental results on two public EHR datasets demonstrate that DuaLK consistently outperforms existing baselines across four clinical prediction tasks. These findings highlight the potential of combining structured medical knowledge with individual-level clinical signals to achieve more accurate and interpretable diagnostic predictions. The source code is publicly available on https://github.com/humphreyhuu/DuaLK.