Civilian marine reactors face a unique set of design challenges in addition to the usual irradiation and thermal-hydraulic limits affecting all reactors. These include requirements for a small core size, long core lifetime, a 20% cap on fissile loading, and limitations on the use of soluble boron. One way to achieve higher burnup/longer core life is to alter the neutron spectrum by changing the hydrogen-to-heavy-metal ratio, thus increasing the conversion of fertile isotopes in the fuel. In this reactor physics study, we optimize the two-dimensional lattice geometry of a 333 MWth soluble-boron-free marine PWR for 18% 235U enriched micro-heterogeneous ThO2-UO2 duplex fuel and 15% 235U enriched homogeneously mixed all-UO2 fuel. We consider two types of coolant: H2O and mixed 80% D2O + 20% H2O. We aim to observe in which spectrum discharge burnup is maximized in order to improve uranium utilization, while satisfying the constraint on moderator temperature coefficient. It is observed that higher discharge burnup for the candidate fuels is achievable by using either a wetter lattice or a much drier lattice than normal, while epithermal lattices are distinctly inferior performers. The thorium-rich duplex fuel exhibits higher discharge burnup potential than the all-UO2 fuel for all moderation regimes for both coolants. The candidate fuels exhibit higher initial reactivity and discharge burnup with the mixed D2O-H2O coolant than with the H2O coolant in the under-moderated regime, whereas these values are lower for the D2O-H2O coolant in the over-moderated regime.