Pyrolysis of waste polymers looks an attractive way for their recycling as valuable hydrocarbons are produced that can be utilized as cleaner energy carriers or petrochemical feedstock. The lumping approach is often used to study the reaction kinetics of such complex systems as the high number of individual chemical species formed during pyrolysis and the several reactions that take place between them make the detailed kinetic modeling of the process often not feasible. Here we propose a two-step identification strategy, which requires no a priori knowledge regarding fast and slow reactions or the temperature dependence of the rate coefficients, to determine the kinetic parameters of pyrolysis and estimate product composition with the required precision using the discrete lumping method. Pyrolysis of a shredded real waste HDPE/PP/LDPE mixture was carried out previously in a laboratory scale two-stage reactor operated in batch mode. The process was investigated at different temperatures; both thermal and thermo-catalytic pyrolysis were studied, the latter on different types of zeolite-based catalysts. Our results indicate that with the suggested lumped model and kinetic identification strategy not only the experimental results can be reproduced but also the essential behavior of different catalysts can be explained. Furthermore, the two stages of the pyrolysis process have also been able to be differentiated. It can be stated that with the proper selection of pseudocomponents, the lumping approach is appropriate for catalyst evaluation and comparison as well, leading to a better understanding of the previous experimental results and the overall pyrolysis process. Hence, the results might also be used during process design or scale-up.