Non-lamellar lyotropic liquid crystalline (LLC) lipid nanoparticles contain internal multidimensional nanostructures such as the inverse bicontinuous cubic and the inverse hexagonal mesophases, which can respond to external stimuli and have the potential of controlling drug release. To date, the internal LLC mesophase responsiveness of these lipid nanoparticles is largely achieved by adding ionizable small molecules to the parent lipid such as monoolein (MO), the mixture of which is then dispersed into nanoparticle suspensions by commercially available poly(ethylene oxide)–poly(propylene oxide) block copolymers. In this study, the Reversible Addition-Fragmentation chain Transfer (RAFT) technique was used to synthesize a series of novel amphiphilic block copolymers (ABCs) containing a hydrophilic poly(ethylene glycol) (PEG) block, a hydrophobic block and one or two responsive blocks, i.e., poly(4-(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)benzyl acrylate) (PTBA) and/or poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA). High throughput small angle X-ray scattering studies demonstrated that the synthesized ABCs could simultaneously stabilize a range of LLC MO nanoparticles (vesicles, cubosomes, hexosomes, inverse micelles) and provide internal particle nanostructure responsiveness to changes of hydrogen peroxide (H2O2) concentrations, pH and temperature. It was found that the novel functional ABCs can substitute for the commercial polymer stabilizer and the ionizable additive in the formation of next generation non-lamellar lipid nanoparticles. These novel formulations have the potential to control drug release in the tumor microenvironment with endogenous H2O2 and acidic pH conditions.