Mixed convection heat transfer of Al_{2}O_{3} nanofluid in a lid-driven square cavity with differentially heated vertical walls is studied numerically with lattice Boltzmann method (LBM). In order to understand the reasons for the conflicting results on heat transfer enhancement in cavity problems, formulation of nondimensional properties and modeling thermophysical properties, in accordance with the relative effects of natural and forced convection flows, are examined. In addition to gain more insight into the physics, one of the goals of the study is to identify the reasons of existing contradictory findings; therefore, a single-phase formulation is adopted as has been the case in the majority of related literature to date. To isolate the effects of thermophysical properties on the results and to maintain the same natural and forced convection effects, all nondimensional parameters are defined using the corresponding thermophysical properties of the fluid under examination. Two different effective thermal conductivity and viscosity models are tested for a range of Reynolds and Rayleigh numbers to investigate their effects on the nanofluid behavior. Depending on the effective viscosity model, an increase or decrease is obtained in the average Nusselt number. It is also illustrated that the relative magnitudes of effective thermal conductivity values for different models do not translate into the heat transfer enhancement due to convective effects. Moreover, it is shown that thermal behavior of nanofluid approaches to the one of base fluid's as the buoyancy driven flow gets stronger, which is independent of the employed effective property models.