According to the Lipid World hypothesis, life on Earth originated with the emergence of amphiphilic assemblies in the form of lipid micelles and vesicles (liposomes). However, the mechanism of appearance of the information molecules (ribozymes/RNA) accompanying that process, considered obligatory for Darwinian evolution, is unclear. We propose a novel scenario of self-sustained Darwinian evolution of the liposomes driven by ever-present natural phenomena: solar UV radiation, day/night cycle, gravity, and the formation of liposomes in an aqueous media. The central tenet of this scenario is the liposomes' encapsulation of the heavy solutes, followed by their gravitational submerging in the water. The submerged liposomes, being protected from the damaging UV radiation, acquire the longevity necessary for autocatalytic replication of amphiphiles, their mutation, and the selection of those amphiphilic assemblies that provide the greatest membrane stability. These two sets of adaptive compositional information (heavy content and amphiphilic assemblies design) generate a population of liposomes with self-replication/reproduction properties, which are amendable to mutation, inheritance, and selection, thereby establishing Darwinian progression. Temporary and spatial expansion of this liposomal population will provide the basis for the next evolutionary step-a transition of accidentally entrapped RNA precursor molecules into complex functional molecules, such as ribozymes/RNA.