A lattice Boltzmann model is proposed to asses the impact of variable molecular transport effects on the heat and mass transfer in a horizontal shallow cavity due to natural convection. The formulation includes a generalized form of the Soret and Dufour mass and heat diffusion (cross diffusion) vectors derived from non-equilibrium thermodynamics and fluctuation theory. Both the individual cross diffusion effect and combined effects on transport phenomena are considered. Results from numerical simulations indicate that Soret mass flux and Dufour energy flux have appreciable effect and sometimes are significant. At the same time, the lattice Boltzmann model has been proved to be adequate to describe higher order effects on energy and mass transfer.