Significance Some soft matter systems behave similarly and some differently. Understanding this is one of the significant challenges in the field. For example, while the splay and bend elastic constants for thermotropic and lyotropic nematic liquid crystals are similar, the twist elastic constant is nearly an order of magnitude smaller in lyotropic nematics. Unfortunately, complete elastic data on lyotropic nematics are restricted to one polymer and two chromonic systems, omitting the most common and highly studied lyotropic surfactant systems. This article reports that a surfactant system of disk-like micelles also possesses an extremely small twist elastic constant, demonstrating that this property is general for lyotropic liquid crystals. The reason likely stems from the higher flexibility of molecular assemblies compared to molecules.