  This work addresses the viability of \textit {Dirac phase leptogenesis}, in a
scenario where the light Majorana neutrinos acquire masses by the inverse
seesaw (ISS) mechanism. We show that, a successful leptogenesis in the ISS,
driven (only) by the Dirac CP phase can be achieved with the involvement of an
unorthodox form of the rotational matrix $R = e^{i{\bf A}} \,\,\,(e^{{\bf A}})$
in the Casas-Ibarra parametrisation. This particular structure of $R$ turns out
to be an artefact in explaining the observed baryon asymmetry of the Universe
in a pure ISS scenario. We detail here the confined regions of the $R$ matrix
parameter space, essential for a successful leptogenesis. The $R$-matrix
parameter space assists in rescuing the ISS parameter space needed for
successful leptogenesis. This finding is otherwise unprecedented in the ISS set
up. Making use of the resulted $R$ matrix parameter space we have calculated
the branching ratio for the LFV decay $\mu \rightarrow e\gamma$. This accounts
for an indirect probe of the $R$-matrix parameter space. The branching ratio
obtained from the leptogenesis parameter space surpasses the existing bound on
the branching ratio that resulted in a scenario of combined effect of linear
and inverse seesaw. We also report here that, for $R = e^{i{\bf A}}$ choice
leptogenesis demands the Dirac CP phase ($\delta$) to oscillate around $\pi/2$,
although for the later choice the constraint on $\delta$ is much relaxed.
