We present a new technique for designing microwave lenses with broadband, true-time-delay response types. The lenses examined in this work are planar structures with circular apertures populated with numerous spatial time-delay units (TDUs). Each TDU is the unit cell of an appropriately designed lowpass frequency selective surface (FSS) that provides a desired time delay over a wide frequency range. The lowpass FSSs used in this paper are either metallo-dielectric or all-dielectric type multi-layer structures. A metallo-dielectric lowpass FSS is composed of a number of capacitive patch layers separated from each other by thin dielectric substrates. An all-dielectric lowpass FSS, on the other hand, is composed of high-epsilon(r) and low-epsilon(r) dielectric substrates cascaded sequentially. Two metallo-dielectric lowpass FSS-based true-time-delay (TTD) lens prototypes and one all-dielectric lowpass FSS-based TTD lens prototype with focal length to aperture diameter ratios of (f/D) 1, 1.5 and 1.3 are designed, fabricated, and experimentally characterized. They respectively operate over a bandwidth of 30%, 50% and 40% without any chromatic aberrations. This is demonstrated experimentally by characterizing the responses of these lenses both in frequency domain and in time domain. Moreover, all of these lenses demonstrates excellent scanning performances with fields of views of +/-60 degrees .