The use of a lead slowing-down spectrometer (LSDS) is considered as a possible option for nondestructive assay of fissile material of used nuclear fuel. The primary objective is to quantify fissile isotopes, particularly 239Pu and 235U, via a direct measurement distinguishing them through their characteristic fission spectra in the LSDS. In this paper, we present several assay measurements performed at the Rensselaer Polytechnic Institute (RPI) to support ongoing feasibility studies of the method and to provide benchmark experiments for Monte Carlo calculations of the assay system. A fresh uranium oxide fuel rod from the RPI Walthousen Reactor Critical Facility, a 239Pu-Be source, and several highly enriched 235U disks were assayed in the LSDS. The characteristic fission spectra were measured with 238U and 232Th threshold fission chambers, which are primarily sensitive to fission neutrons with energies above the threshold. Despite the constant neutron and gamma background from the Pu-Be source and the intense interrogation neutron flux, the LSDS system was able to measure the characteristic 235U and 239Pu responses. All measurements were compared to Monte Carlo simulations complementing previous modeling-based studies. It is shown that the available simulation tools and models are well suited to simulate the assay. An absolute calibration technique of the LSDS, which is required to perform quantitative measurements of the assayed fissile materials, is presented.