Polariton lasers are coherent light sources based on the condensation of exciton-polaritons in semiconductor microcavities, which occurs either in the kinetic or thermodynamic (Bose-Einstein) regime. Besides their fundamental interest, polariton lasers have the potential of extremely low operating thresholds. Here, we demonstrate ultra-low threshold polariton lasing at room temperature, using an all-dielectric, GaN membrane-based microcavity, with a spontaneously-formed zero-dimensional trap. The microcavity is fabricated using an innovative method, which involves photo-electrochemical etching of an InGaN sacrificial layer and allows for the incorporation of optimally-grown GaN active quantum wells inside a cavity with atomically-smooth surfaces. The resulting structure presents near-theoretical Q-factors and pronounced strong-coupling effects, with a record-high Rabi splitting of 64 meV at room-temperature. Polariton lasing is observed at threshold carrier densities 2.5 orders of magnitude lower than the exciton saturation density. Above threshold, angle-resolved emission spectra reveal an ordered pattern in k-space, attributed to polariton condensation at discrete levels of a single confinement site. This confinement mechanism along with the high material and optical quality of the microcavity, accounts for the enhanced performance of our polariton laser, and pave the way for further developments in the area of robust room temperature polaritonic devices.