We demonstrate simple and intuitive methods, for dispersion optimization and characterization of highly nonlinear fiber (HNLF) for use in four-wave-mixing (FWM) based time lens applications. A composite dispersion-flattened HNLF is optimized for high bandwidth time lens processing, by segmentation to mitigate FWM impairments due to dispersion fluctuations. The fiber is used for FWM conversion of 32 WDM-channels with 50 GHz spacing in a time lens, with -4.6 dB total efficiency, and <1 dB per-channel efficiency difference. The novel characterization method is based on two tunable continuous-wave lasers. The method is experimentally verified to predict the spectral output profile of time lenses for broadband multicarrier input, with detailed numerical simulations for support.