Hybrid-phase metal-organic frameworks (MOFs) are a class of intriguing heterostructures for diverse applications, the properties of which are governed by their chemical composition, framework topology, and morphology. Herein, we report the structural and morphological evolution of flexible MOFs induced by the lattice change of template during heteroepitaxial growth. We demonstrate that the epitaxially grown flexible Fe-MOFs can be varied from one structure to another to adapt to the lattice of the template Zr-MOFs. Thus, flexible Fe-MOFs with similar chemical compositions and topology can be epitaxially grown on different Zr-MOFs over huge lattice constant gradient. We also demonstrate that the morphology of the heterostructures is affected by the degree of lattice difference between the template MOFs and the epitaxial MOFs. The reported results could pave the way toward the rational design of hybrid-phase MOFs guided by the principles of reticular chemistry.