Additive manufacturing of solid-state batteries is advantageous for improving the power density by increasing the geometric complexity of battery components, such as electrodes and electrolytes. In the present study, bulk three-dimensional Li1+xAlxTi2-x(PO4)3 (LATP) electrolyte samples were prepared using the laser powder bed fusion (L-PBF) additive manufacturing method. Li3PO4 (LPO) was added to LATP to compensate for lithium vaporization during processing. Chemical compositions included 0, 1, 3, and 5 wt. % LPO. Resulting ionic conductivity values ranged from 1.4 x 10-6 to 6.4 x 10-8 S cm-1, with the highest value for the sample with a chemical composition of 3 wt. % LPO. Microstructural features were carefully measured for each chemical composition and correlated with each other and with ionic conductivity. These features and their corresponding ranges include: porosity (ranging from 5 to 19%), crack density (0.09 to 0.15 mm/mm2), concentration of residual LPO (0 to 16%), and concentration and Feret diameter of secondary phases, AlPO4 (11 to 18%, 0.40 to 0.61 µm) and TiO2 (9 to 11%, 0.50 to 0.78). Correlations between the microstructural features and ionic conductivity ranged from -0.88 to 0.99. The strongest negative correlation was between crack density and ionic conductivity (-0.88), confirming the important role that processing defects play in limiting the performance of bulk solid-state electrolytes. The strongest positive correlation was between the concentration of AlPO4 and ionic conductivity (0.99), which is attributed to AlPO4 acting as a sintering aid and the role it plays in reducing the crack density. Our results indicate that additions of LPO can be used to balance competing microstructural features to design bulk three-dimensional LATP samples with improved ionic conductivity. As such, refinement of the chemical composition offers a promising approach to improving the processability and performance of functional ceramics prepared using binderless, laser-based additive manufacturing for solid-state battery applications.