Post-processing of Ti6Al4V lattice structures fabricated using selective laser melting (SLM) was performed using hot isostatic pressing (HIPing) and heat treatment (HT) to mitigate the undesired effect of rapid cooling during SLM. Oxygen diffusion during post-processing had a significant influence on the microstructure and subsequently the mechanical properties of the lattices. Oxygen content analysis was conducted to confirm the oxygen diffusion through the strurts’ peripheries. The effect of oxygen diffusion during the HIPing and sub-transus HT (600–800 °C) regimes on the phase transformation, failure mechanisms, and mechanical properties of the lattices was investigated. Results revealed that the transformation of the originally formed α′ martensite was dependent on the post-processing temperature. This transformation resulted in a decrease in yield strength. The decrease in failure strain (ductility) for all treated conditions was related to oxygen diffusion, forming near-surface α-case.