Application of lower hybrid (LH) current drive in tokamak plasmas can induce both co- and countercurrent directed changes in toroidal rotation, depending on the core q profile. For discharges with q(0) <1, rotation increments in the countercurrent direction are observed. If the LH-driven current is sufficient to suppress sawteeth and increase q(0) above unity, the core toroidal rotation change is in the cocurrent 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 dependence on magnetic shear.