X-ray diffraction measurements to characterize phase transitions of dynamically compressed high-Z matter at Mbar pressures require both sufficient photon energy and fluence to create data with high fidelity in a single shot. Large-scale laser systems can be used to generate x-ray sources above 10 keV utilizing line radiation of mid-Z elements. However, the laser-to-x-ray energy conversion efficiency at these energies is low, and thermal x-rays or hot electrons result in unwanted background. We employ polycapillary x-ray lenses in powder x-ray diffraction measurements using solid target x-ray emission from either the Z-Beamlet long-pulse or the Z-Petawatt (ZPW) short-pulse laser systems at Sandia National Laboratories. Polycapillary lenses allow for a 100-fold fluence increase compared to a conventional pinhole aperture while simultaneously reducing the background significantly. This enables diffraction measurements up to 16 keV at the few-photon signal level as well as diffraction experiments with ZPW at full intensity.