We report the first-time use of the Aqueye+ and Iqueye instruments to record lunar occultation events. High time resolution recordings in different filters have been acquired for several occultations taken from 2016 January through 2018 January with Aqueye+ at the Copernicus telescope and Iqueye at the Galileo telescope in Asiago, Italy. Light curves with different time bins were calculated in post-processing and analyzed using a least-square model-dependent method. A total of nine occultation light curves were recorded, including one star for which we could measure for the first time the size of the chromosphere (mu Psc) and one binary star for which discrepant previous determinations existed in the literature (SAO 92922). A disappearance of Alf Tau shows an angular diameter in good agreement with literature values. The other stars were found to be unresolved, at the milliarcsecond level. We discuss the unique properties of Aqueye+ and Iqueye for these kind of observations, namely the simultaneous measurement in up to four different filters thanks to pupil splitting, and the unprecedented time resolution well exceeding the microsecond level. This latter makes Aqueye+ and Iqueye suitable to observe not just occultations by the Moon, but also much faster events such as, e.g., occultations by artificial screens in low orbits. We provide an outlook of future possible observations in this context.