The supercritical CO2 (sCO2) Brayton cycle for the lead-cooled fast reactor (LFR) is an ideal power generation system for the distributed energy supply in remote islands. To figure out the optimal operating modes of the MW-scale sCO2 LFR unit in different load demands, this work performs a dynamic simulation based on the developed control modules. A parametric analysis is conducted about the effects of rotational speed, split ratio, and main gas temperature on the dynamic characteristics. Control strategies are further studied based on the thermodynamic performance and safety under four variable temperature load regulation modes and three fixed temperature rapid load regulation modes. Results show that the tracking αopt mode has the highest average net efficiency (ηnetav) of 19.13 %. The tracking αsafe mode allows compressors to operate in the safest range by sacrificing a little ηnetav. Excellent load change rates are revealed by using the main circuit regulating valve control mode and the turbine bypass control mode, with −12.48 %Pe/min & 11.92 %Pe/min, and −8.25 %Pe/min & 9.70 %Pe/min, respectively. Though the load change rate of the RS control mode is −3.96 %Pe/min & 3.47 %Pe/min, its ηnetav is higher. Our work guides the efficient, flexible, and safe operation of the sCO2 LFR unit.