A new broadband double-shell axial symmetric lens with integral feed is proposed, where the refraction interfaces from both shells are adequately shaped to comply with a frequency stable radiation pattern template and frequency stable phase centre position across a broad 1:3 frequency band. When used to illuminate a reflector in quasi-optical systems, those lens features provide reasonably constant and high reflector aperture efficiency versus frequency. The lens is compatible with the integration of ultra-wideband uniplanar printed feeds at its base and equally broadband mixing devices, like the Hot Electron Bolometer (HEB), although an alternative feed is used for concept demonstration. Measurements on a scaled lab lens prototype operating from 30 GHz to 90 GHz, have confirmed stable performance versus frequency, with only ±1dB directivity variation, and better than 94% Gaussicity. Simulations to evaluate the illumination of an off-set parabolic reflector by this lens radiation pattern, confirmed reasonably constant aperture efficiency in the order of 78% across the 100% bandwidth.