The simulation of soot evolution is a problem of relevance for the development of low-emission aero-engine combustors. Apart from detailed CFD approaches, it is of importance to develop models with modest computational cost so a large number of geometries can be explored, especially in view of the need to predict engine-out soot particle size distributions to meet future regulations. In this work, the Incompletely Stirred Reactor (ISR) theory is extended to a reactor network formulation, based on the Conditional Moment Closure (CMC) combustion model. An ISR is a volume V that is inhomogeneous in terms of mixture fraction but is characterized by homogeneous conditional averages, such as temperature and soot mass fraction conditioned on the mixture fraction having a particular value. A network of ISRs (ISRN) is then deployed to separately capture soot production and oxidation regions exhibiting different degrees of micro-mixing rates and residence times, as typically observed in practical combustors. The network is positioned and clustered around the mesh of a reference CFD simulation providing the ISRN with the average flow and mixing fields. Here, the ISRN approach is demonstrated on a single sector lean-burn model combustor operating on Jet A fuel and in pilot only mode, which corresponds to conditions of a lean-burn engine at part load. The results of the ISRN are compared with data previously obtained with LES-CMC coupled with detailed chemistry for dodecane and a two-equation model for soot. The comparison provides a satisfactory assessment of the method reliability, demonstrating the ability of the ISRN approach to replicate soot emission both in terms of mean location and magnitude while ensuring high computational efficiency. The ISRN approach can consequently be used to explore soot evolution utilizing complex chemical mechanisms and comprehensive soot models that otherwise would be intractable to couple with current CFD methods. In this direction, real fuel chemistry and a detailed physicochemical sectional soot model are combined to investigate the sensitivity of ISRN predictions.