  In this paper we continue the investigation of the lattice gas model. The
main improvement is that we use two strengths for bonds: one between like
particles and another between unlike particle to implement the
isospin-dependence of nuclear force. The main effect is the elimination of
unphysical clusters, like the dineutron or diproton. It is therefore a better
description of nuclear system. Equation of state in mean field theory is
obtained for nuclear matter as well as for $N\ne Z$ systems. Through numerical
and analytical calculation we show that the new model maintains all the
important features of the older model. We study the effect of the Coulomb
interaction on multifragmentation of a compound system of A=86, Z=40 and also
for A=197, Z=79. For the first case the Coulomb interaction has small effect.
For the latter case the effect is much more pronounced but typical signatures
of the lattice gas model such as a minimum (maximum) in the value of $\tau$
($S_2$) are still obtained but at a much lower temperature.
