The emplacement dynamics of lava flows on a slope is investigated using theoretical analyses and laboratory experiments for the case where a fixed volume of lava is rapidly released and propagates downhill as a two-dimensional flow. When the lava has no internal yield strength, we identify four dynamical flow regimes that can arise: an inertial slumping regime, a horizontal viscous regime, a sloping viscous regime, and a crust yield strength regime that finally stops the flow. When the lava has an internal yield strength, it can also flow in a sloping viscoplastic regime which is accurately predicted by a simple box model that we derive. Our results are applied to predict the propagation downhill of various volumes of two typical lavas: a Hawaiian lava with no internal yield strength and a Mount Etna lava with an internal yield strength. In particular, we find that sloping flows of the Mount Etna lava are stopped by the surface crust strength rather than the internal yield strength.