We address unresolved questions of the energetics and mechanism of lipid droplet (LD) biogenesis, and of the role of caveolins in the endoplasmic reticulum (ER) and in mature LDs. LDs are eukaryotic repositories of neutral lipids, which are believed to be synthesised in the ER. We investigate the effects of a curvature-inducing protein, caveolin-1, on the formation and structure of a spontaneously aggregated triolein (TO) lipid lens in a flat lipid bilayer using molecular dynamics (MD) simulations. A truncated form of caveolin-1 (Cav1) localises on the interface between the spontaneously formed TO aggregate and the bulk bilayer, and thins the bilayer at the edge of the aggregate, which may contribute to lowering the energy barrier for pinching off the aggregate from the host bilayer. Simulations of fully mature LDs do not conclusively establish the optimal localisation of Cav1 in LDs, but when Cav1 is in the LD core, the distribution of both neutral lipids in the LD core, and of phospholipids on the engulfing monolayer are altered significantly. Our simulations provide an unprecedented molecular description of the distribution and dynamics of various lipid species in both mature LDs and in the nascent LD inside the bilayer.