The isoscaling behavior is investigated using the isotopic/isobaric yields from the equilibrated thermal source which is prepared by the lattice gas model (LGM) for lighter systems with A = 36. The isoscaling parameters α and -β are observed to drop with temperature for the LGM with the asymmetric nucleon-nucleon potential. However, the isoscaling parameters do not show 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 system. PACS numbers: 25.70.Pq, 24.10.Pa, 05.70.JkIsoscaling has been observed in a variety of reactions under the conditions of statistical emission and equal temperature recently by Tsang et al [1,2,3]. This kind of scaling means that the ratio R 21 (N,Z) of the yields of a given fragment (N,Z) exhibits an exponential dependence on N and Z when these fragments are produced in two reactions with different isospin asymmetry, but at the same temperature. Experimentally the isoscaling has been explored in various reaction mechanisms, ranging from the evaporation [1], fission [4,5] and deep inelastic reaction at low energies to the projectile fragmentation [6,7] and multi-fragmentation at intermediate energy [1,8,9]. While, the isoscaling has been extensively examined in different theoretical frameworks, ranging from dynamical model, such as Anti-symmetrical Molecular Dynamics model [10] and BUU model [8], to statistical models, such as Expansion Emission Source Model and statistical multi-fragmentation model [2,3,11,12]. From all these reaction mechanisms and models, it looks that isoscaling is a robust probe to relate with the symmetrical term of the nuclear equation of state.Typically, the investigations of isoscaling focused on yields of light fragments with Z=2-8 originating from deexcitation of massive hot systems produced using reactions of mass symmetric projectile and target at intermediate energies, such as 112,124 Sn + 112,124 Sn in Michigan State University (MSU) data [1,2,3] or by reactions of high-energy light particle with massive target nucleus [11,13]. In a recent article [6], the isoscaling using the heavy projectile residue from the reactions of 25 MeV/nucleon 86 Kr projectiles with 124 Sn, 112 Sn and 64 Ni, 58 Ni targets which was performed at Texas A&M University (TAMU) and the isoscaling phenomenon on the full sample of fragments emitted by the hot thermally equilibrated quasi-projectiles with mass A = 20-30 are also reported [7].