A design optimization workflow for the casing of a 1.5 stage axial turbine is implemented through a novel endwall surface definition, towards improving the turbine efficiency. The new non-axisymmetric casing design compares favourably to an established diffusion design technique. The workflow uses an axial turbine three-dimensional Reynolds Averaged Navier-Stokes model built in OpenFOAM Extend 3.2 with the k-omega Shear Stress Transport turbulence closure. Computer-based optimization of the surface topology using a Kriging surrogate model automates the design process. The designs are optimized using the total pressure loss across the full stage as the target function. Axial turbine performance gains are obtained from the workflow, which persist both at the design condition and off-design. These gains are used to project the impact of equivalent design improvements to the power turbine of a representative Natural Gas liquefaction plant cycle. Cycle Coefficient of Performance enhancements between 2.05% and 2.923% are obtained, at design and at off design conditions. Implementing these performance improvements has the potential to reduce carbon dioxide emissions by 165.54 tonnes per year at design and by 108.18 tonnes per year at off design, in a representative Natural Gas liquefaction plant.