In this study, low calorie triacylglycerols (TAG) of MLM type (containing a medium-chain fatty acid, M, at positions sn-1,3 and a long-chain fatty acid at position sn-2) were produced by acidolysis of virgin olive oil with caprylic (C8:0) or capric (C10:0) acids, in solvent-free media. The heterologous sn-1,3 regioselective Rhizopus oryzae lipase produced by the methylotrophic yeast Pichia pastoris (r-ROL) was immobilized in Amberlite IRA 96® (rROL-IRA) and used as biocatalyst. Acidolysis was optimized as a function of temperature and molar ratio (C:8/TAG or C10:0/TAG), by response surface methodology. The production of new TAG, the consumption of C8:0 or C10:0, and triolein were evaluated. From the response-surfaces fitted to the experimental data points, no optimal points were observed inside the experimental region. The highest consumption of TAGs, free fatty acids and triolein (the major TAG) were achieved at 29 °C and molar ratio (MR) of 2:1 at 24 h reaction time. For the system with virgin olive oil and caprylic acid (C8:0), the highest consumption of TAG was 76.9% while for the system with virgin olive oil and C10:0, 85.6 % of TAG consumption was observed. Also for the system with virgin olive oil and capric acid, 70.7 and 68.8% consumption of initial TAGs and triolein, respectively, were observed for MR of 1.6:1 and at 40 °C, corresponding to a star point of the experimental design. The production of structured TAG from olive oil and medium chain fatty acids (caprylic and capric acids) catalyzed by the heterologous Rhizopus oryzae lipase immobilized in Amberlite IRA 96 is a promising alternative to the high-cost immobilized commercial lipases for MLM production.