Interest is steadily growing for multi-rotor wind turbine concepts. This type of wind turbine offers a practical solution for scaling issues of large wind turbine components and for the reduction of costs associated with manufacturing, logistics, and maintenance. However, the literature lacks thorough knowledge of the dynamic performance of multi-rotor wind turbine concepts installed on floating platforms. Previous research studied the dynamic response of a two-rotor wind turbine concept mounted on a spar-type floating platform (2WT). Platform yaw motion is a significant dynamic factor directly caused by differential turbulence intensity experienced by the two hubs coupled with the distribution of thrust loads on the tower structure. Blade-pitch control analysis also showed how the 2WT yaw response is extremely sensitive to the control strategy employed. In this work, a linear quadratic regulator (LQR) is used to design an optimal controller for the 2WT prototype. Three LQR gain schedules corresponding to three operation regions are considered. An in-house tool for the dynamic analysis of multi-rotor floating wind turbines is used for linear state-space extraction and dynamic analysis. The control performance in different load conditions is assessed against the baseline OC3 proportional-integral (PI) control strategy and a PI-P control strategy in a previous article presented by the authors.