LPBF-manufactured Inconel718 lattices with six cubic and hexagonal structures and with two material microstructures (as-built, without γ” precipitation, and heat-treated, with γ” precipitates, but with similar cell/grain size, shape and texture) were compressed at room temperature and at 600 °C. The behavior of the base material under identical microstructure and test conditions was also investigated using dedicated LPBF-manufactured specimens with single strut gauges. Irrespective of topology, precipitation led to a transition in the lattice mechanical behavior from bending-dominated to stretch-dominated, which was associated to a change in the strut deformation mode from plastic hinging to elastic buckling, as well as to a decrease in the base material strain to fracture. For all topologies investigated, precipitation led to lattice strengthening, consistent with particle-strengthening of the base material. Additionally, high temperature straining resulted both in a decrease in the lattice yield strength, consistent with softening of the base material, and in a reduction in the width of the stress oscillations in the stretch-dominated lattices, which is associated to the decrease in the base material ductility. This work proves that material microstructure influences strongly the behavior of additively manufactured architectured structures and that it must be considered as a design criterion for performance optimization.