In this study we analyze two groups of Mediterranean salt lenses: ''mid-life'' lenses, typically 1-2 years old, observed in the Canary Basin, and younger Meddies from the Iberian Basin. In contrast to turbulent features, vortex lenses have a clear coherent structure in the temperature and salinity fields. This physical property supports the hypothesis that a mathematical description with only a few degrees of freedom may exist. We use nonlinear transformation of variables to find a unique function describing vertical profiles at different locations inside the lens. When this function is found, its existence is considered as ''self-similarity'' of the lens structure. We also found a common function that describes each group of Meddy, Canary and Iberian, and noted a remarkable difference between the groups. A possible reason for this result might lie in the difference in lens age. Iberian lenses are in a more juvenile state and may go through adjustment transformations before turning into more stable mid-life vortices. The developed parameterization is used to calculate radii and integral heat and salt contents of Meddles.