The ability to solve jointly lithology units and elastic parameters has been shown to improve characterization when a detailed background model is difficult to build. Petrophysical parameters can also be resolved if lithology driven rock model is available. For anisotropic formations, using joint litho-petro-elastic (LPE) inversion enables us to assign anisotropy information to the lithology units. This proves to be very beneficial for AVA/AVAz inversion where the azimuthal invariant anisotropic parameter space (the vertical transverse isotropy (VTI)) is not resolvable independently from shear information. In many cases, neglecting to account for anisotropy will lead to inferior characterization of anisotropic plays. Anisotropic LPE inversion enables anisotropic characterization by identifying the anisotropic formation as a part of the inversion process. Moreover, LPE inversion also provide estimates of the petrophysical parameter space and therefore honor the relation between the anisotropic elasticity, lithology and petrophysical parameters. This study review the LPE inversion workflow and show how the anisotropic LPE inversion in VTI media is used to derive jointly elastic properties, lithology, and petrophysical parameters of the Wolfcamp shale play. We also demonstrate the importance of including anisotropy in the inversion and show that isotropic inversion poorly delineated the lithology of the play.