  We present a deperturbation analysis of the spin-orbit coupled $\rm
A^1\Sigma^+$ and $\rm b^3\Pi_{0^+}$ states of LiRb based on the rovibrational
energy levels observed previously by photoassociation spectroscopy in bosonic
$^7$Li$^{85}$Rb molecule. Using the genetic algorithm, we fit the potential
energy curves of the $\rm A^1\Sigma^+$ state and the $\rm b^3\Pi$ state into
point-wise form. We then fit these point-wise potentials along with the
spin-orbit coupling into expanded Morse oscillator functional form and optimise
analytical parameters based on the experimental data. From the fitted results,
we calculate the transition dipole moment matrix elements for transitions from
the rovibrational levels of the coupled $\rm A^1\Sigma^+$-$\rm b^3\Pi_{0^+}$
state to the Feshbach state and the absolute rovibrational ground state for
fermionic $^6$Li$^{87}$Rb molecule. Based on the calculated transition dipole
moment matrix elements, several levels of the coupled $\rm A^1\Sigma^+$-$\rm
b^3\Pi_{0^+}$ state are predicted to be suitable as the intermediate state for
stimulated Raman adiabatic passage transfer from the Feshbach state to the
absolute rovibrational ground state. In addition, we also provide a similar
estimation for ${\rm B}^1\Pi$-${\rm c}^3\Sigma_1^+$-${\rm b}^3\Pi_1$ state
based on available $ab\ initio$ interaction potentials.
