The rectified bulk photovoltaic effect (BPVE) in noncentrosymmetric semiconductors, also called shift current, is considered promising for optoelectronic devices, terahertz emission, and possibly solar energy harvesting. A clear understanding of the shift current mechanism and search for materials with large shift current is, therefore, of immense interest. ABC semiconductors LiZnX (X=N, P, As, and Sb) can be stabilized in cubic as well as hexagonal morphologies lacking inversion symmetry - an ideal platform to investigate the significant contributing factors to shift current, such as the role of structure and chemical species. Using density-functional calculations properly accounting for the electronic bandgaps, the shift current conductivities in LiZnX (X=P, As, Sb) are found to be approximately an order of magnitude larger than the well-known counterparts and peak close to the maximum solar radiation intensity. Notably, hexagonal LiZnSb shows a peak shift current conductivity of about -75μA/V2 and Glass coefficient of about -20×10-8 cm/V, comparable to the highest predicted values in literature. Our comparative analysis reveals a quantitative relationship between the shift current response and the electronic polarization. These findings not only posit Li-Zn-based ABC semiconductors as viable material candidates for potential applications but also elucidates key aspects of the structure-BPVE relationship.