Lattice materials can be designed through their microstructure while concurrently considering fabrication feasibility. Here, we propose two types of composite lattice materials with enhanced resistance to buckling: (a) hollow lattice materials fabricated by a newly developed bottom-up assembly technique and the previously developed thermal expansion molding technique and (b) hierarchical lattice materials with foam core sandwich trusses fabricated by interlocking assembly process. The mechanical performance of sandwich structures featuring the two types of lattice cores was tested and analyzed theoretically. For hollow lattice core material, samples from two different fabrication processes were compared and both failed by nodal rupture or debonding. In contrast, hierarchical lattice structures failed by shear buckling without interfacial failure in the sandwich struts. Calculations using established analytical models indicated that the shear strength of hollow lattice cores could be optimized by judicious selection of the thickness of patterned plates. Likewise, the shear strength of hierarchical foam core truss cores could be maximized (with minimal weight) through design of truss geometry. The bottom-up assembly technique could provide a feasible way for mass production of lattice cores, but the design about how to assembly is critical. Hierarchical lattice cores with foam sandwich trusses should be a suitable choice for future lightweight material application.