Stimuli-responsive materials are crucial to advance controlled delivery systems for drugs and catalysts. Lyotropic liquid crystals (LLCs) have well-defined internal structures suitable to entrap small molecules and can be broken up into low-viscosity dispersions, aiding their application as delivery systems. In this work, we demonstrate the first example of light-responsive cubic LLC dispersions, or cubosomes, using photoswitchable amphiphiles to enable external control over the LLC structure and subsequent on-demand release of entrapped guest molecules. Azobenzene photosurfactants (AzoPS), containing a neutral tetraethylene glycol head group and azobenzene-alkyl tail, are combined (from 10-30 wt %) into monoolein-water systems to create LLC phases. Homogenization of the bulk LLC forms dispersions of particles, ∼200 nm in diameter with internal bicontinuous primitive cubic phases, as seen using small-angle X-ray scattering and cryo-transmission electron microscopy. Notably, increasing the AzoPS concentration leads to swelling of the cubic lattice, offering a method to tune the internal nanoscale structure. Upon UV irradiation, AzoPS within the cubosomes isomerizes within seconds, which in turn leads to squeezing of the cubic lattice and a decrease in the lattice parameter. This squeeze mechanism was successfully harnessed to enable phototriggerable release of trapped Nile Red guest molecules from the cubosome structure in minutes. The ability to control the internal structure of LLC dispersions using light, and the dramatic effect this has on the retention of entrapped molecules, suggests that these systems may have huge potential for the next-generation of nanodelivery.