One major drawback associated with single-walled carbon nanotubes (SWNTs) in the liquid phase is their hydrophobicity-induced aggregation, which prevents utilization of the unique physical and chemical properties of single SWNTs. Recently it has been found that lysophospholipids, or single-tailed phospholipids, can readily form supramolecular complexes with SWNTs and the resultant SWNT solubility is superior to that provided by nucleic acids, proteins, and surfactants such as sodium dodecyl sulfate. Using transmission electron microscopy, lysophospholipids were observed forming striations on SWNTs in a vacuum. Although the morphology of the striations seemingly favors the hemimicellular model, serious doubts remain about the arrangement of individual lipids within the striations. Here we present an in silico study of the binding of zwitterionic lysophosphatidylcholine to an SWNT. We present compelling evidence that the binding of lipid surfactants to cylindrical nanostructures in the liquid phase does not obey any of the three popular models in the literature. Understanding the binding of lipid amphiphiles to SWNTs facilitates the bottom-up design of novel nanostructures for supramolecular chemistry and nanotechnology and fuels new field studies of nanotoxicity and nanomedicine.