Wave propagation in optical mediums greatly depends on the materials of which the guides are composed. Among the other forms of optical mediums, liquid crystals are both inhomogeneous and optically anisotropic in nature, and exhibit strong electro-optic behavior, which allows alternation in their optical properties under the influence of external electrical fields. These features make optical fibers containing liquid crystals greatly useful for fabricating many optical devices for practical applications. As such, the analytical investigation of wave propagation through liquid crystal optical fibers, particularly a three-layer fiber with radially anisotropic liquid crystal material in the outermost clad section, remains interesting. The power confinement in the liquid crystal section of such fibers can be enhanced for these to be efficiently used in optical coupling and/or sensing applications. Furthermore, a control over the dispersion characteristics, and, hence, the confinement of power, in such fibers may be imposed by making the guide even more complex in the form of introducing a conducting sheath helix structure at the core-inner clad interface.