  New boson representation of the su(2)-algebra proposed by the present authors
for describing the damped and amplified oscillator is examined in the Lipkin
model as one of simple many-fermion models. This boson representation is
expressed in terms of two kinds of bosons with a certain positive parameter. In
order to describe the case of any fermion number, third boson is introduced.
Through this examination, it is concluded that this representation is well
workable for the boson realization of the Lipkin model in any fermion number.
