<p>The thermodynamic, mechanical, and dynamical stabilities of Zr_n+1PbB_n (<i>n</i> = 1, 2, 3) MAX phase borides were confirmed through first-principles calculations. Stability assessments were carried out by evaluating formation energies, phonon dispersion curves, and elastic constants. The elastic constants revealed anisotropic mechanical behavior, with higher compressibility along the z-axis for Zr₂PbB and Zr₄PbB₃, and along the x-axis for Zr₃PbB₂. The direction dependent values of Young’s modulus, compressibility, shear modulus and Poisson’s ratio are visualized by 2D and 3D representations. Thermal conductivity analysis indicated that Zr₂PbB and Zr₄PbB₃ exhibit superior heat dissipation capabilities, while all phases demonstrate low minimum thermal conductivity, making them promising candidates for thermal barrier coatings (TBC). Interestingly, distinct mechanical and thermal properties were observed between phases with odd and even n-values, highlighting the impact of structural variations on material performance. Regarding tensile strength, the maximum stresses along the [001] direction were found to be 14.57 GPa, 13.67 GPa, and 13.73 GPa at strains of 22%, 18%, and 14% for Zr₂PbB, Zr₃PbB₂, and Zr₄PbB₃, respectively. In comparison, along the [110] direction, the corresponding maximum stresses were slightly lower, reaching approximately 13.50 GPa, 12.80 GPa, and 12.95 GPa at lower strains. Zr₂PbB exhibits the highest tensile strength and strain tolerance along the [001] direction. Additional thermal parameters, including Debye, melting temperatures, heat capacities and thermal expansion coefficient were examined to understand their suitability for extreme environments. The n-index governing the layer stacking sequence plays a key role in determining the mechanical and thermal performance of Zr_n+1PbB_n MAX phases, with even-n structures showing enhanced properties due to their favorable symmetry.</p>