Controlling the growth morphology of fluid instabilities is challenging because of their self-amplified and nonlinear growth. The viscous fingering instability, which arises when a less viscous fluid displaces a more viscous one, transitions from exhibiting dense-branching growth characterized by repeated tip splitting of the growing fingers to dendritic growth characterized by stable tips in the presence of anisotropy. We controllably induce such a morphology transition by shear-enhancing the anisotropy of nematic liquid crystal solutions. For fast enough flow induced by the finger growth, the intrinsic tumbling behavior of lyotropic chromonic liquid crystals can be suppressed, which results in a flow alignment of the material. This microscopic change in the director field occurs as the viscous torque from the shear flow becomes dominant over the elastic torque from the nematic potential and macroscopically enhances the liquid crystal anisotropy to induce the transition to dendritic growth.