This paper introduces Tree-Like Analytical Queries (TLAQ) model for supporting enhanced big healthcare data analytics via an innovative concept, the so-called lazy aggregations. Given a hierarchical tree-like aggregate query, which fully supports advanced big data analytics tools, according to the lazy aggregation paradigm, data ranges of two parent-child nodes do not satisfy the containment relation, thus opening the door to detailed implementations of target medical investigation processes (e.g., in the context of epidemiological research). The latter innovation turns to be extremely useful in modern big healthcare data analytics, as proofed in this paper. We finally provide a comprehensive case study about the potentialities of the TLAQ analytical model on top of a real-life case study deriving from a reference EU H2020 research project.