Human milk fat (HMF) triacylglycerols (TAGs) mainly contain palmitic acid esterified at the sn-2 position while oleic and other unsaturated fatty acids are located at positions sn-1,3. This study aimed at the production of HMF substitutes (HMFS) by lipase-catalyzed acidolysis of tripalmitin with oleic acid, in a solvent-free medium. Burkholderia cepacia lipase (BCL) was immobilized in silica (prepared with protic or aprotic ionic liquids) by covalent binding or encapsulation and used as biocatalyst. The supports and immobilized biocatalysts were characterized by FTIR, TGA, and SEM. Molecular docking analysis showed that BCL preferentially attacks oleic acid rather than tripalmitin, due to the lower free energy of hydrophobic binding with this acid (−6.5 kcal·mol−1) than with tripalmitin (5.4 kcal·mol−1). Therefore, the tripalmitin attack by BCL and subsequent HMFS production only occurs after the binding to most of the oleic acid molecules. The highest acidolysis activity was obtained with BCL immobilized by covalent binding in prepared silica with aprotic ionic liquid. A central composite rotatable design, as a function of temperature (58–72 °C) and oleic acid/tripalmitin molar ratio (MR = 2:1–6.8:1), was performed for acidolysis optimization. Under optimized conditions (58 °C and MR = 4:1 or 60 °C and MR = 2:1), the oleic acid incorporation of 28 mol.% was achieved after 48 h.