High-precision molecular-dynamics (MD) data are reported for the shear viscosity {eta} of the Lennard-Jones liquid at its triple point, as a function of the shear rate {dot {epsilon}} for a large system ({ital N}=2048). The Green-Kubo (GK) value {eta}({dot {epsilon}}=0)=3.24{plus minus}0.04 is estimated from a run of 3.6{times}10{sup 6} steps (40 nsec). We find no numerical evidence of a {ital t}{sup {minus}3/2} long-time tail for the GK integrand (stress-stress time-correlation function). From our nonequilibrium MD results, obtained both at small and large values of {dot {epsilon}}, a consistent picture emerges that supports an analytical (quadratic at low shear rate) dependence of the viscosity on {dot {epsilon}}.