Lipid nanoparticles (LNP) are promising soft matter nanomaterials for drug delivery applications. In spite of their interest, little is known about the supramolecular organization of the components of these self-assembled nanoparticles. Here, we present a molecular dynamics simulation study, employing the Martini coarse-grain forcefield, of self-assembled LNPs made by tripalmitin lipid in water. We also study the adsorption of Tween 20 surfactant as a protective layer on top of the LNP. We show that, at 310 K (the temperature of interest in biological applications), the structure of the lipid nanoparticles is similar to that of a liquid droplet, in which the lipids show no nanostructuration and have high mobility. We show that, for large enough nanoparticles, the hydrophilic headgroups develop an interior surface in the NP core that stores liquid water. The surfactant is shown to organize in an inhomogeneous way at the LNP surface, with patches with high surfactant concentrations and surface patches not covered by surfactant.