Mechanical behavior of additively manufactured lattice materials has been mainly investigated under uniaxial compression, while their performance under uniaxial and multiaxial tension are yet to be understood. To address this gap, a generic elastoplastic homogenization scheme with continuum damage model is developed, and three different lattice materials, namely cubic, modified face-center cubic and body-center cubic, are analyzed under uniaxial, biaxial and triaxial tension. The influence of micro-architecture on the material's failure behavior as well as its macroscopic mechanical performance is thoroughly discussed. For validation, a set of uniaxial tensile experiments are conducted on functionally graded cubic lattice samples that are additively manufactured using Electron Beam Melting (EBM) process. Digital image correlation technique is employed to obtain the macroscopic stress–strain curves, and manufacturing imperfections are inspected using light omitting microscopy. It turns out that the behavior of as-built samples could substantially differ from numerical predictions. Thus, a defect-informed numerical model is employed to accommodate the effect of imperfections. The outcome is in a very good agreement with experimental data, indicating that with proper input data, the developed scheme can accurately predict the mechanical and failure behavior of a given lattice material.