High porosity level lattice structures made using electron beam powder bed fusion additive manufacturing (EBPBF) need to be sufficiently strong and the understanding of the mechanical anisotropy of the structures is important for the design of orthopedic implants. In this work, the combined effects of loading direction (LD), cell orientation, and strut irregularity associated with EBPBF of Ti6Al4V alloy lattices on the mechanical behavior of the lattices under compressive loading have been studied. Three groups of simple cubic unit cell lattices were EBPBF made, compressively tested, and examined. The three groups were [001]//LD lattices, [011]//LD lattices, and [111]//LD lattices. Simulation has also been conducted. Yield strength (σy-L) values of all lattices determined experimentally have been found to be comparable to the values predicted by simulation; thus, EBPBF surface defects do not affect σy-L. σy-L of [001]//LD lattices is 1.8–2.0 times higher than those of [011]//LD and [111]//LD lattices. The reason for this is shown to be due to the high stress concentrations in non-[001]//LD samples, causing yielding at low loading levels. Furthermore, plastic strain (εp) at ultimate compression strength of [001]//LD samples has been determined to be 4–6 times higher than the values of non-[001]//LD samples. Examining the tested samples has shown cracks more readily propagating from EBPBF micro-notches in non-[001]//LD samples, resulting in low εp.