The detection of a broadband signal consistent with an extended exosphere of very small (less than 20-30 nm radius) dust grains was recently reported from the Ultraviolet and Visible Spectrometer (UVS) onboard the Lunar Atmosphere and Dust Environment Explorer (LADEE). Such emission was especially enhanced during the Quadrantids – a major annual meteoroid stream encountered by the Earth-Moon system. The Lyman-Alpha Mapping Project (LAMP) FUV spectrograph onboard the Lunar Reconnaissance Orbiter (LRO) carried out a follow-up campaign in order to search for backscattering of sunlight from lunar exospheric dust, and investigate its dependence on meteoroid stream activity. With a wavelength range of 57 – 196 nm, LRO/LAMP complements the LADEE/UVS wavelength range (230 – 810 nm) since it is able to place additional constraints on the size and abundance of such grains. In particular, Mie scattering modeling predicts that the long wavelength region of LAMP (170 – 190 nm) is best suited to detect nanodust particles, due to a combination of high scattering efficiency and rapidly increasing solar radiance with wavelength. LRO/LAMP performed a series of inertial pointing stares as close as possible to the anti-sunward direction to maximize the backscattering efficiency or intensity from any exospheric dust. These stares also pointed at a region of the sky devoid of bright stars in order to minimize any background signal. The observations were targeted to coincide with the peak in activity of two major meteoroid streams: the Geminids (December 14th 2015) and the Quadrantids (January 4th 2016). The polar orbit of LRO allows the LAMP line-of-sight to cross the day/night terminator near the poles. We compare spectra from the same orbit, before and after crossing the terminator near the North Pole, to search for any change in the brightness between times when the LAMP line-of-sight was fully illuminated and times when it was partially shadowed by the Moon. In the preliminary data reduction, no such difference in brightness was observed during either of the meteoroid streams. We discuss the implications of these non-detections for the interpretation of LADEE/UVS measurements, as well as the upper limits for nanodust abundances inferred from LAMP.