Data cubes, frequent itemsets, and concept lattices are the core data models in the fields of data warehouse, data mining, and formal concept analysis, respectively. Although they are applied to different fields of data analysis or mining, they all essentially establish similar partial-order structures in the form of lattices. However, previous work does not systematically and thoroughly study their correlation that will be greatly beneficial, say enhancing each other. To address this main concern, this paper deeply studies the lattice structure construction process of data cubes, frequent itemsets and concept lattices, and then generalizes them as a unified model by finding mapping among them. Further, we explore the wide spectrum application scenarios by exemplifying their fusion algorithms which means we may compute one using another with more efficient complexity by leveraging the mapping between them. Experiments on real datasets demonstrate the efficiency of the fusion algorithm, where the fusion algorithm achieves the highest improvement rate of 51.9%.