The concept of closed nuclear fuel cycle seems to be the most promising options for the efficient usage of the nuclear energy resources. However, it can be implemented only in fast breeder reactors of the IVth generation, which are characterized by the fast neutron spectrum. The lead-cooled fast reactor (LFR) was defined and studied on the level of technical design in order to demonstrate its performance and reliability within the European collaboration on ELSY (European Lead-cooled System) and LEADER (Lead-cooled European Advanced Demonstration Reactor) projects. It has been demonstrated that LFR meets the requirements of the closed nuclear fuel cycle, where plutonium and minor actinides (MA) are recycled for reuse, thereby producing no MA waste. In this study, the most promising option was realized when entire Pu + MA material is fully recycled to produce a new batch of fuel without partitioning. This is the concept of a fuel cycle which asymptotically tends to the adiabatic equilibrium, where the concentrations of plutonium and MA at the beginning of the cycle are restored in the subsequent cycle in the combined process of fuel transmutation and cooling, removal of fission products (FPs), and admixture of depleted uranium. In this way, generation of nuclear waste containing radioactive plutonium and MA can be eliminated. The paper shows methodology applied to the LFR equilibrium fuel cycle assessment, which was developed for the Monte Carlo continuous energy burnup (MCB) code, equipped with enhanced modules for material processing and fuel handling. The numerical analysis of the reactor core concerns multiple recycling and recovery of long-lived nuclides and their influence on safety parameters. The paper also presents a general concept of the novel IVth generation breeder reactor with equilibrium fuel and its future role in the management of MA.