This study presents an investigation on the axial negative thermal expansion of alpha-PbAlBO4 and beta-PbAlBO4. Polycrystalline and single-crystal samples were prepared by solid-state synthesis method, characterized by temperature- and pressure-dependent X-ray and neutron diffraction experiments. The axial negative linear compressibility (NLC) is known for the alpha-polymorph, although structurally different the beta-polymorph also shows similar NLC phenomenon. The lattice thermal expansion was described using the first-order Gruneisen equation of state, where the vibrational energy was calculated using the Debye-Einstein-Anharmonicity model. The density functional theory (DFT)-based phonon density of states and Raman spectra helped to choose the characteristic frequency to model the metric parameters. Lattice thermal expansion was additionally simulated in the quasi-harmonic approximation using the plane-wave DFT approach at the PBEsol level. The apparent departure of the quasi-harmonic approximation model has been discussed in terms of associated thermodynamic functions. The interplay between the topology-induced negative cross-compliance and anisotropic Gruneisen parameter has been identified as the driving force for the axial negative linear compressibility and axial negative thermal expansion.