This work presents a numerical study of natural convection in a right-angled triangular cavity filled with a Cu–water nanofluid, using the single-relaxation-time lattice Boltzmann method (SRT-LBM). The aim is to evaluate the influence of copper nanoparticles on thermal performance under different heating conditions and flow regimes. Two configurations are considered: Case 1, where the inclined wall is heated, and Case 2, where the vertical wall is heated. In both cases, the opposing wall is cold, and the third wall is adiabatic. The study explores a wide range of Rayleigh numbers (103 ≤ Ra ≤ 106) and nanoparticle volume fractions (0% ≤  \(\varphi\)  ≤ 7%). The thermophysical properties of the nanofluid are calculated using Corcione’s empirical model, taking into account temperature-dependent variations in thermal conductivity and viscosity. The thermal behavior is analyzed in terms of isotherms, streamlines, and the average Nusselt number. Results show that the addition of nanoparticles enhances heat transfer, particularly in the conduction-dominated regime (low Ra), where the effect of increased thermal conductivity outweighs the rise in viscosity. At higher Rayleigh numbers, however, an optimal concentration emerges—approximately 6% for Ra = 105 and 4% for Ra = 106, beyond which the negative impact of increased viscosity begins to limit convective transport. Comparative analysis between the two heating cases reveals that the orientation of the heated wall plays a crucial role in optimizing natural convection heat transfer. The numerical results are validated against benchmark data from the literature, confirming the robustness and accuracy of the SRT-LBM approach.