Turbulence over the ocean at heights relevant to modern offshore wind turbines, i.e., up to 300 m or more, is not well studied. It is important to know the properties of this turbulence because it is responsible for most of the dynamic loads on these structures, and consequently it is relevant to how the latter should be designed. This data description paper explains the efforts made to provide measurements of this offshore turbulence using five Doppler lidars.