Isoscaling behavior is investigated using the isotopic and isobaric yields from an equilibrated thermal source which is prepared by the lattice gas model (LGM) for lighter systems with A=36. The isoscaling parameters alpha and beta are observed to drop with temperature for the LGM with the asymmetric nucleon-nucleon potential. However, the isoscaling parameters do not show a temperature dependence for the LGM with the symmetric nucleon-nucleon potential. The relative neutron or proton density shows a nearly linear relation with the N/Z (neutron to proton ratio) of the system.