The methanol–glycerol co-feeding during the induction stage for heterologous protein production in Pichia pastoris has shown significant productive applications. Available model analysis applied to this dual-limited condition is scarce and normally does not consider the interaction effects between the substrates. In this work, a dual-limited growth model of P. pastoris considering an interactive kinetic effect was applied to an optimised fed-batch process production of heterologous Rhizopus oryzae lipase (ROL). In the proposed model, the growth kinetics on glycerol is fully expressed, whereas methanol kinetics is modulated by the co-metabolisation of glycerol, resulting in an enhancing effect of glycerol-specific growth rate. The modelling approach of fed-batch cultures also included the methanol volatilisation caused by the aeration that was found to be a not-negligible phenomenon. The model predicts the ability of P. pastoris to keep control of the methanol concentration in the broth during ROL-optimised production process in fed batch and fits satisfactorily the specific cell growth rate and ROL production. Implications of interaction effect are discussed applying the general procedure of modelling approach.