Application of lower hybrid current drive (LHCD) in tokamak plasmas can induce both co- and counter-current directed changes in toroidal rotation, depending on the core magnetic shear, s. For discharges with s > 1, rotation increments in the countercurrent direction are observed. If the LH driven current is sufficient to suppress sawteeth and reduce the central s below unity, the core toroidal rotation change is in the co-current direction. This change in sign of the rotation increment is consistent with a change in sign of the residual stress (the divergence of which constitutes an intrinsic torque that drives the flow) through its dependance on s.