Proper selection of the power conversion cycle is a very important step in the design of a nuclear reactor. Due to the higher core outlet temperature (~550°C) compared to that of light water reactors (~300°C), a wide portfolio of power cycles is available for the lead alloy fast reactor (LFR). Comparison of the following cycles for the LFR was performed: superheated steam (direct and indirect), supercritical steam, helium Brayton, and supercritical CO2 (S-CO2) recompression. Heat transfer from primary to secondary coolant was first analyzed and then the steam generators or heat exchangers were designed. The direct generation of steam in the lead alloy coolant was also evaluated. The resulting temperatures of the secondary fluids are in the range of 530-545°C, dictated by the fixed space available for the heat exchangers in the reactor vessel. For the direct steam generation situation, the temperature is 312°C. Optimization of each power cycle was carried out, yielding net plant efficiency of around 40% for the superheated steam cycle while the supercritical steam and S-CO2 cycles achieved net plant efficiency of 41%. The cycles were then compared based on their net plant efficiency and potential for low capital cost. The superheated steam cycle is a very good candidate cycle given its reasonably high net plant efficiency and ease of implementation based on the extensive knowledge and operating experience with this cycle. Although the supercritical steam cycle net plant efficiency is slightly better than that of the superheated steam cycle, its high complexity and high pressure result in higher capital cost, negatively affecting plant economics. The helium Brayton cycle achieves low net plant efficiency due to the low lead alloy core outlet temperature, and therefore, even though it is a simpler cycle than the steam cycles, its performance is mediocre in this application. The prime candidate, however, appears to be the S-CO2 recompression cycle, because it achieves about the same net plant efficiency as the supercritical steam cycle and is significantly simpler than the steam cycles. Moreover, the S-CO2 cycle offers a significantly higher potential for an increase in efficiency than steam cycles, after better materials allow the LFR operating temperatures to be increased. Therefore, the S-CO2 is chosen as the reference cycle for the LFR, with the superheated or supercritical steam cycles as backups if the S-CO2 cycle development efforts do not succeed.