The demand of lattice structures for medical applications is increasing due to their ability to accelerate the osseointegration process, to reduce the implant weight and the stiffness. Selective laser melting (SLM) process offers the possibility to manufacture directly complex lattice applications, but there are a few studies that have focused on biocompatible Ti6Al7Nb alloy. The purpose of this work was to investigate the physical-mechanical properties and the microstructure of three dissimilar lattice structures that were SLM-manufactured by using Ti6Al7Nb powder. In particular, the strut morphology, the fracture characterization, the metallographic structure, and the X-ray phase identification were analyzed. Additionally, the Gibson-Ashby prediction model was adapted for each lattice topology, indicating the theoretical compressive strength and Young modulus. The resulted porosity of these lattice structures was approximately 56%, and the pore size ranged from 0.40 to 0.91 mm. Under quasi-static compression test, three failure modes were recorded. Compared to fully solid specimens, the actual lattice structures reduce the elastic modulus from 104 to 6-28 GPa. The struts surfaces were covered by a large amount of partial melted grains. Some solidification defects were recorded in struts structure. The fractographs revealed a brittle rupture of struts, and their microstructure was mainly α' martensite with columnar grains. The results demonstrate the suitability of manufacturing lattice structures made of Ti6Al7Nb powder having unique physical-mechanical properties which could meet the medical requirements.