It was shown recently that a solid-to-solid phase transitions (α-to-β, gel-to-crystal), typical for many lipid substances, can lead to formation of nanoporous network inside lipid micro-particles dispersed in aqueous surfactant solutions (Cholakova et al. ACS Nano 2020, 14, 8594). These nanopores are spontaneously infused by the aqueous phase when appropriate combination of water-soluble and oil-soluble surfactants is applied. As a result, the initial lipid micro-particles can spontaneously burst into much smaller nanoparticles, just by cooling and heating of the initial dispersion. Under certain conditions, the infused aqueous phase is entrapped in the moment of lipid particle melting and double emulsion of type water-in-oil-in-water (W/O/W) is formed. The current study aims to clarify how the composition of the lipid micro-drops and surfactants affect the observed phenomena. Selected mixtures of monoacid triglycerides are studied systematically. The results show that the bursting efficiency usually decreases when the complexity of the lipid mixture increases, due to the expanded temperature interval for lipid melting. Nevertheless, complete particle bursting and lipid nanoparticles with diameters down to 20 nm are formed even for the most complex lipid compositions under appropriate conditions. The key mechanisms leading to efficient fragmentation and double emulsion formation are clarified, and the main governing factors are explored. On this basis, we reveal that the system behavior can be switched between complete particle bursting and W/O/W emulsion formation by: (1) Change in the cooling and heating rates without any changes in the chemical composition, (2) Change in the concentration of oil-soluble surfactant, and/or (3) Change in the phase in which the oil-soluble surfactant is introduced initially. Thus, we have formulated guiding rules to control the formation of lipid nanoparticles and W/O/W emulsions with triglyceride mixtures promising multiple potential applications.