Recent developments in low-noise, large-area CCD detectors have renewed interest in radiographic systems that use a lens to couple light from a scintillation screen to a detector. The lenses for this application must have very large numerical apertures and high spatial resolution over a FOV. This paper expands on our earlier work by applying the principles of task-based assessment of image quality to development of meaningful figures of merit for the lenses. The task considered in this study is detection of a lesion in a mammogram, and the figure of merit used is the lesion detectability, expressed as a task-based signal-to-noise ratio (SNR), for a channelized Hotelling observer (CHO). As in the previous work, the statistical model accounts for the random structure in the breast, the statistical properties of the scintillation screen, the random coupling of light to the CCD, the detailed structure of the shift-variant lens point spread function (PSF), and Poisson noise of the X-ray flux. The lenses considered range from F/0.9 to F/1.2. All yield nominally the same spot size at a given field. Among the F/0.9 lenses, some of them were designed by conventional means for high resolution and some for high contrast, and the shapes of the PSF differ considerably. The results show that excessively large lens numerical apertures do not improve the task-based SNR but dramatically increase the optics fabrication cost. Contrary to common wisdom, high-contrast designs have higher task-based SNRs than high-resolution designs when the signal is small. Additionally, we constructed a merit function to successfully tune the lenses to perform equally well anywhere in the FOV.