  In quantum lattice systems with geometric frustration, particles cannot move
coherently due to destructive interference between tunnelling processes. Here
we show that purely local, Markovian dissipation can induce mobility and
long-range first-order coherence in frustrated lattice systems that is entirely
generated by incoherent processes. Interactions reduce the coherences and
mobility but do not destroy them. These effects are observable in experimental
implementations of driven-dissipative lattices with a flat band and non-uniform
dissipation.
