The lithium beam diagnostic at JET provides information about the electron density in the scrape-off-layer and pedestal region. The density is reconstructed from the spatial profile of the 2p line emission of a collisionally excited neutral lithium beam (energy typically 60keV), which is injected into the plasma edge from the top of the machine parallel to the direction of the Z coordinate. The spatial and temporal resolution achieved at JET is Dt10ms, DZ1cm. The beam emission is observed using a periscope. The reconstruction uses a probabilistic inversion procedure which is based on a collisional-radiative model for the beam-plasma interaction.