We provide proof-of-principle illustration of lasing in a two-dimensional polariton topological insulator. Topological edge states may arise in a structured polariton microcavity under the combined action of spin-orbit coupling and Zeeman splitting in the magnetic field. Their properties and lifetime are strongly affected by gain. Thus, gain concentrated along the edge of the insulator can counteract intrinsic losses in such a selective way that the topologically protected edge states become amplified, while bulk modes remain damped. When gain is compensated by nonlinear absorption the metastable nonlinear edge states are formed. Taking a triangular structure instead of an infinite edge we observed persistent topological currents accompanied by the time-periodic oscillations of the polariton density.