In this study, we investigate the impact of vertical wind shear and wind speed inversions on the power production of a floating offshore wind turbine. Using nacelle-mounted wind lidar data from a 6 MW turbine at the Hywind Scotland wind farm, we analyse inflow conditions and turbine performance during summer and autumn. The wind climatology shows that 33 % of examined cases exhibit non-standard wind profiles within the rotor-swept area, including negative shear and wind speed inversions. These conditions significantly affect power production, particularly below rated wind speeds, with negative shear profiles causing reductions of up to 20 % compared to the reference power curve. Our findings demonstrate that deviations from the logarithmic wind profile at the operating height range of modern wind turbines, are frequent in deep-water offshore environments and can introduce substantial bias in power curve verification. Nacelle-mounted wind lidars provide critical insight into these inflow characteristics, enabling improved performance assessment of floating offshore wind turbines. The results highlight the need for measurement strategies that capture wind conditions across the full rotor-swept area, which can be achieved through nacelle-mounted wind lidar instruments.