A process of directed UV photo-curing was previously developed for producing periodic thiol-ene lattices, with potential for use in lightweight structures. The present study probes the compressive response of two families of such lattices: with either one or two layers of a pyramidal truss structure. The principal goals are to assess whether the strengths of the lattices attain levels predicted by micromechanical models and to ascertain the role of lattice heterogeneities. These goals are accomplished through characterization of the lattice geometries via X-ray computed tomography and optical microscopy, measurements of the mechanical properties of the constituent thiol-ene and those of the lattices, and strain mapping on the lattices during compressive loading. Comparisons are also made with the properties of the thiol-ene alone, produced in bulk form. We find two lattice heterogeneities: (i) variations in strut diameter, from smallest at the top surface where the incident UV beam impinges on the monomer bath to largest at the bottom surface; and (ii) variations in physical and mechanical properties, with regions near the top surface being stiffest and strongest and exhibiting the highest glass transition temperature. Finally, we find that the measured strengths of the lattices are in accord with the model predictions when the geometric and material property variations are taken into account in the micromechanical models.