Crude olive pomace oil (OPO) is a by-product of olive oil extraction. In this study, low-calorie structured triacylglycerols (TAGs) were produced by acidolysis of crude OPO with medium-chain fatty acids (caprylic, C8:0; capric, C10:0) or interesterification with their ethyl ester forms (C8EE, C10EE). These new TAGs present long-chain fatty acids (L) at position sn-2 and medium-chain fatty acids (M) at positions sn-1,3 (MLM). Crude OPO exhibited a high acidity (12.05–28.75% free fatty acids), and high contents of chlorophylls and oxidation products. Reactions were carried out continuously in a packed-bed bioreactor for 70 h, using sn-1,3 regioselective commercial immobilized lipases (Thermomyces lanuginosus lipase, Lipozyme TL IM; and Rhizomucor miehei lipase, Lipozyme RM IM), in solvent-free media at 40 °C. Lipozyme RM IM presented a higher affinity for C10:0 and C10EE. Lipozyme TL IM preferred C10:0 over C8:0 but C8EE over C10EE. Both biocatalysts showed a high activity and operational stability and were not affected by OPO acidity. The New TAG yields ranged 30–60 and the specific productivity ranged 0.96–1.87 g NewTAG/h.g biocatalyst. Lipozyme RM IM cost is more than seven-fold the Lipozyme TL IM cost. Therefore, using Lipozyme TL IM and crude acidic OPO in a continuous bioreactor will contribute to process sustainability for structured lipid production by lowering the cost of the biocatalyst and avoiding oil refining.