Lamellar gel networks are creamy formulations extensively used in cosmetics and pharmaceutics. The basic units of these networks are lipid bilayers assembled from mixtures of fatty alcohols, surfactants and water. Despite being an essential step for the preparation of the dispersions, the nature of the mixtures at high temperature has defied understanding. Here, we show by atomistic molecular dynamics simulations that aqueous mixtures of cetyl (C16OH) and stearyl (C18OH) alcohols, and cetyl-trimethylammonium chloride (CTAC) lead to fluid bilayers, the units of the lamellar Lα phase. By providing a consistent numerical simulation model able to describe the structure and properties of fatty alcohol lamellae stabilized by surfactant, our work paves the way for the elucidation of the forces regulating this family of industrially important gels.