The use of copper complexes for redox and oxidative-based mechanisms in therapeutic strategies is an important field of multidisciplinary research. Here, a novel Cu(II) complex [Cu(TPMA)(Phen)](ClO) (Cu-TPMA-Phen, where TPMA = tris-(2-pyridylmethyl)amine and Phen = 1,10-phenanthroline) was studied using both the free and encapsulated forms. A hollow pH-sensitive drug-delivery system was synthesized, characterized, and used to encapsulate and release the copper complex, thus allowing for the comparison with the free drug. The human neuroblastoma-derived cell line NB100 was treated with 5 μM Cu-PMA-Phen for 24 h, pointing to the consequences on mono- and polyunsaturated fatty acids (MUFA and PUFA) present in the membrane lipidome, coupled with cell viability and death pathways (3-(4,5-dimethylthiazol-2-yl)-5-(3-carboxymethoxyphenyl)-2-(4-sulfophenyl)-2-tetrazolium viability assay, flow cytometry, microscopy, caspase activation). In parallel, the Cu-TPMA-Phen reactivity with the fatty acid moieties of phospholipids was studied using the liposome model to work in a biomimetic environment. The main results concerned: (i) the membrane lipidome in treated cells, involving remodeling with a specific increase of saturated fatty acids (SFAs) and a decrease of MUFA, but not PUFA; (ii) cytotoxic events and lipidome changes did not occur for the encapsulated Cu-TPMA-Phen, showing the influence of such nanocarriers on drug activity; and (iii) the liposome behavior confirmed that MUFA and PUFA fatty acid moieties in membranes are not affected by oxidative and isomerization reactions, proving the different reactivities of thiyl radicals generated from amphiphilic and hydrophilic thiols and Cu-TPMA-Phen. This study gives preliminary but important elements of copper(II) complex reactivity in cellular and biomimetic models, pointing mainly to the effects on membrane reactivity and remodeling based on the balance between SFA and MUFA in cell membranes that are subjects of strong interest for chemotherapeutic activities as well as connected to nutritional strategies.