The asymmetric next-nearest neighbor (NNN) Ising model has been studied for describing the self-diffusion of adsorbate atoms at low temperature, furthermore adding a relevant ingredient in such a regime, i.e., a finite value Q for the trapping potential barrier. The Monte Carlo technique leads to the components of the (tracer) diffusion coefficient. An interesting feature is seen : a "V-Lambda transition" occurs at half-coverage (c=0.5) when the temperature is lowered. The activation energy (obtained from an Arrhenius plot) is seen to be varying as a function of coverage, and is not symmetrical with respect to c=0.5. The anisotropy of the diffusion and the change in its pattern as a function of the temperature and coverage are presented and discussed. Monte Carlo snapshots are shown at various coverage and temperature values.