Three-dimensional Monte Carlo neutronics calculations for the last mirror-beam duct system for a laser-driven fusion power reactor conceptual design, where a three-section duct with focusing mirrors and right angle bends for the last two beam reflections is modeled. The estimate of neutron leakage flux after the second beam reflection is on the order of 1014 n/(m2⋅s). Even though less in magnitude than the flux at the end point of neutral beam injectors in tokamak designs, reported in the range of 1017 n/(m2⋅s), this still leads to a neutron dose rate of 106 remjh after the second beam bend. Since space is not at a premium as in the case of magnet shields for magnetic confinement systems, minimum-cost lead mortar or concrete can be used as shielding materials instead of other minimum-thickness costly materials. An energy leakage rate of 4.6 MW of 14-MeV neutrons per beam precludes the use of concrete behind the last mirror, suggesting the use of a secondary blanket composed of a lead acetate solution with immersed Boral (Al + B4C) sheets. Boral as a penetration shielding material is found to reduce the thermal group flux around the penetration by two to three orders of magnitude, compared to aluminum, and is recommended as a duct lining material for both inertial and magnetic fusion systems. Neutron heating rates and radiation damage parameters for the duct liner compare to those at the front face of the last mirror and first wall, and will require similar elaborate thermal-hydraulic and mechanical designs.