We present the results of calculations determining the cross sections for indirect dissociative recombination of LiH$_2^+$ + $e^-$. These calculations employ multichannel quantum defect theory and Fanos rovibrational frame transformation technique to obtain the indirect DR cross section in the manner described by Ref.cite{hamilton}. We use textit{ab initio} electron-molecule scattering codes to calculate quantum defects. In contrast to H$_3^+$, the LiH$_2^+$ molecule exhibits considerable mixing between rotation and vibration; however, by incorporating an exact treatment of the rovibrational dynamics of the LiH$_2^+$, we show that this mixing has only a small effect on the observed DR rate. We calculate a large DR rate for this cation, 4.0 $times$ 10$^{-7}$ cm$^{3}$ s$^{-1}$ at 1 meV incident electron energy.
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