  Measuring the full distribution of individual particles is of fundamental
importance to characterize many-body quantum systems through correlation
functions at any order. Here we demonstrate the possibility to reconstruct the
momentum-space distribution of three-dimensional interacting lattice gases
atom-by-atom. This is achieved by detecting individual metastable Helium atoms
in the far-field regime of expansion, when released from an optical lattice. We
benchmark our technique with Quantum Monte-Carlo calculations, demonstrating
the ability to resolve momentum distributions of superfluids occupying $10^5$
lattice sites. It permits a direct measure of the condensed fraction across
phase transitions, as we illustrate on the superfluid-to-normal transition. Our
single-atom-resolved approach opens a new route to investigate interacting
lattice gases through momentum correlations.
