Random anti-reflection structured surfaces (rARSS) have been reported to improve transmittance of optical-grade fused silica planar substrates to values greater than 99%. These textures are fabricated directly on the substrates using reactive-ion/inductively-coupled plasma etching (RIE/ICP) techniques, and often result in transmitted spectra with no measurable interference effects (fringes) for a wide range of wavelengths. The RIE/ICP processes used in the fabrication process to etch the rARSS is anisotropic and thus well suited for planar components. The improvement in spectral transmission has been found to be independent of optical incidence angles for values from 0° to ±30°. Qualifying and quantifying the rARSS performance on curved substrates, such as convex lenses, is required to optimize the fabrication of the desired AR effect on optical-power elements. In this work, rARSS was fabricated on fused silica plano-convex (PCX) and plano-concave (PCV) lenses using a planar-substrate optimized RIE process to maximize optical transmission in the range from 500 to 1100 nm. An additional set of lenses were etched in a non-optimized ICP process to provide additional comparisons. Results are presented from optical transmission and beam propagation tests (optimized lenses only) of rARSS lenses for both TE and TM incident polarizations at a wavelength of 633 nm and over a 70° full field of view in both singlet and doublet configurations. These results suggest optimization of the fabrication process is not required, mainly due to the wide angle-of-incidence AR tolerance performance of the rARSS lenses. Non-optimized recipe lenses showed low transmission enhancement, and confirmed the need to optimized etch recipes prior to process transfer of PCX/PCV lenses. Beam propagation tests indicated no major beam degradation through the optimized lens elements. Scanning electron microscopy (SEM) images confirmed different structure between optimized and non-optimized samples. SEM images also indicated isotropically-oriented surface structures on both types of lenses.