Design and fabrication of beam-based lattices using 3D printing technology have enabled the development of biomedical implants with mechanically efficient scaffolds. For instance, bone tissue scaffolds are engineered implants that could benefit from multi-directional stiffness tuning in relation to the complex loadings of the body. Here, we introduce beam-based lattices with height-adjustable BC-Tetra unit cell designs with different configurations for tuning the elastic modulus along different loading axes. The BC-Tetra unit cell has a tetragonal organization with a square base and adjustable height. Unit cells were designed with a beam diameter of 0.8 mm, porosities of approximately 50% and 70%, and varied unit cell heights for each porosity. Lattices were built during the stereolithography process with E-Shell 600 material that is a biocompatible methacrylic acid-based polymer. Mechanical compression experiments were conducted to investigate the effects of varied BC-Tetra unit cell designs on the longitudinal and transverse elastic moduli of the lattice structures. Mechanical compression testing indicates that the longitudinal elastic modulus of the structures increases with the unit cell height, whereas the transverse elastic modulus decreases. Thus, the adjustment of unit cell height allows tailoring of elastic modulus in multiple directions to ensure implants can adjust the host bone loading while mitigating stress shielding. These results contribute to better design decisions for 3D printed lattice structures with specified mechanical properties that provide new dimensions for biomedical implant design.