Abstract This work aims to produce triacylglycerols (TAG) containing a medium‐chain fatty acid (M) at positions sn‐1,3 and a long‐chain fatty acid (L) at sn‐2 position, i.e. TAG of MLM type, by acidolysis of virgin olive oil with caprylic (C8:0) or capric (C10:0) acids, catalyzed by 1,3‐selective Rhizopus oryzae heterologous lipase (rROL) immobilized in Eupergit® C and modified sepiolite. This lipase was produced by the methylotrophic yeast Pichia pastoris. Reactions were performed at 25 and 40 °C, for 24 h, either in solvent‐free or in n‐hexane media, at a molar ratio 1:2 (olive oil:free fatty acid). Higher incorporations of C8:0 (21.6 mol%) and C10:0 (34.8 mol%) into the TAG were attained in solvent‐free media, at 40 °C, when rROL immobilized in Eupergit® C was used. In organic media, at 40 °C, only 15.9 and 14.1 mol%, incorporation of C8:0 or C10:0 were, respectively observed. Lower incorporations were attained for both acids (3.4–7.0 mol%) when native ROL (nROL) in both supports and rROL in modified sepiolite were used. rROL in Eupergit® C maintained its activity during the first four or three 23‐h batches, respectively when C8:0 (half‐life time, t1/2 = 159 h) or C10:0 (t1/2 = 136 h) were used, decreasing thereafter following a time delay model.