Glyceryl monooleate (GMO) is one of the most popular amphiphilic lipids, which, in the presence of different amounts of water and a proper amount of stabilizer, can promote the development of well defined, thermodynamically stable nanostructures, called lyotropic liquid crystal dispersions. The aim of this study is based on the design, characterization, and evaluation of the cytotoxicity of lyotropic liquid crystal nanostructures containing a model anticancer drug such as doxorubicin hydrochloride. The drug is efficiently retained by the GMO nanosystems by a remote loading approach. The nanostructures prepared with different non-ionic surfactants (poloxamers and polysorbates) are characterized by different physico-chemical features as a function of several parameters, i.e., serum stability, temperature, and different pH values, as well as the amount of cryoprotectants used to obtain suitable freeze-dried systems. The nanostructures prepared with poloxamer 407 used as a stabilizer show an increased toxicity of the entrapped drug on breast cancer cell lines (MCF-7 and MDA-MB-231) due to their ability to sensitize multidrug-resistant (MDR) tumor cells through the inhibition of specific drug efflux transporters. Moreover, the interaction between the nanostructures and the cells occurs after just a few hours, evidencing a huge cellular uptake of the nanosystems.