The combination of strain and bioprocess engineering strategies should be considered to obtain the highest levels of recombinant protein production (RPP) while assuring product quality and process reproducibility of heterologous products. In this work, two complementary approaches were investigated to improve bioprocess efficiency based on the yeast P. pastoris. Firstly, the performance of two Candida rugosa lipase 1 producer clones with different gene dosage under the regulation of the constitutive PGAP were compared in chemostat cultures with different oxygen-limiting conditions. Secondly, hypoxic conditions in carbon-limited fed-batch cultures were applied by means of a physiological control based on the respiratory quotient (RQ). Stirring rate was selected to maintain RQ between 1.4 and 1.6, since it was found to be the most favorable in chemostat. As the major outcome, between 2-fold and 4-fold higher specific production rate (qP) values were observed when comparing multicopy clone (MCC) and single-copy clone (SCC), both in chemostat and fed-batch. Additionally, when applying oxygen limitation, between 1.5-fold and 3-fold higher qP values were obtained compared with normoxic conditions. Thus, notable increases of up to 9-fold in the production rates were reached. Furthermore, transcriptional analysis of certain key genes related to RPP and central carbon metabolism were performed. Results seem to indicate the presence of a limitation in post-transcriptional protein processing steps and a possible transcription attenuation of the target gene in the strains with high gene dosage. The entire approach, including both strain and bioprocess engineering, represents a relevant novelty involving physiological control in Pichia cell factory and is of crucial interest in bioprocess optimization, boosting RPP, allowing bioproducts to be economically competitive in the market, and helping develop the bioeconomy.