The paper investigates the fabrication of Selective Laser Melting (SLM) titanium alloy Ti6Al4V micro-lattice structures for the production of lightweight components. Specifically, the pillar textile unit cell is used as base lattice structure and alternative lattice topologies including reinforcing vertical bars are also considered. Detailed characterizations of dimensional accuracy, surface roughness, and micro-hardness are performed. In addition, compression tests are carried out in order to evaluate the mechanical strength and the energy absorbed per unit mass of the lattice truss specimens made by SLM. The built structures have a relative density ranging between 0.2234 and 0.5822. An optimization procedure is implemented via the method of Taguchi to identify the optimal geometric configuration which maximizes peak strength and energy absorbed per unit mass.