Floating offshore wind opens new possibilities for harnessing wind energy in deeper waters where it is not feasible to install traditional fixed-bottom turbines. Accessing deeper waters enables the utilization of stronger and more consistent wind resources, potentially leading to higher energy production. However, one of the challenges of floating offshore wind is the impact of increased motions on floating turbine’s power. This paper addresses this challenge by investigating wind field reconstruction and motion compensation algorithms when using a nacelle lidar to characterize floating turbine inflow wind speed. The fully instrumented TetraSpar floating demonstrator with a 3.6 MW wind turbine and a nacelle lidar, offers a unique opportunity to investigate the effect of motions on power production. Observations from real measurements are complemented with numerical simulations, highlighting that motion-compensating for mean tilt angle is an effective correction for 10 min average power performance measurements. Results showed that mean tilt angles causing the lidar beams to shift upwards, result in overestimation of the estimated hub height wind speed if no motion compensation is applied. The paper also assesses the impact of motions induced by different sea states on power production.