  We study transport in twisted bilayer graphene and show that electrostatic
barriers can act as valley splitters, where electrons from the $K$ ($K'$)
valley are transmitted only to e.g.\ the top (bottom) layer, leading to
valley-layer locked currents. We show that such a valley splitter is obtained
when the barrier varies slowly on the moir\'e scale and induces a Lifshitz
transition across the junction, i.e.\ a change in the Fermi surface topology.
Furthermore, we show that for a given valley the reflected and transmitted
current are transversely deflected, as time-reversal symmetry is effectively
broken in each valley separately, resulting in valley-selective transverse
focusing at zero magnetic field.
