A turbulent lifted slot-jet flame is studied using direct numerical simulation (DNS). A one-step chemistry model is employed with a mixture-fraction-dependent activation energy which can reproduce qualitatively the dependence of the laminar burning rate on the equivalence ratio that is typical of hydrocarbon fuels. The basic structure of the flame base is first examined and discussed in the context of earlier experimental studies of lifted flames. Several features previously observed in experiments are noted and clarified. Some other unobserved features are also noted. Comparison with previous DNS modelling of hydrogen flames reveals significant structural differences. The statistics of flow and relative edge-flame propagation velocity components conditioned on the leading edge locations are then examined. The results show that, on average, the streamwise flame propagation and streamwise flow balance, thus demonstrating that edge-flame propagation is the basic stabilisation mechanism. Fluctuations of the edge locations and net edge velocities are, however, significant. It is demonstrated that the edges tend to move in an essentially two-dimensional (2D) elliptical pattern (laterally outwards towards the oxidiser, then upstream, then inwards towards the fuel, then downstream again). It is proposed that this is due to the passage of large eddies, as outlined in Su et al. (Combust. Flame, vol. 144 (3), 2006, pp. 494–512). However, the mechanism is not entirely 2D, and out-of-plane motion is needed to explain how flames escape the high-velocity inner region of the jet. Finally, the time-averaged structure is examined. A budget of terms in the transport equation for the product mass fraction is used to understand the stabilisation from a time-averaged perspective. The result of this analysis is found to be consistent with the instantaneous perspective. The budget reveals a fundamentally 2D structure, involving transport in both the streamwise and transverse directions, as opposed to possible mechanisms involving a dominance of either one direction of transport. It features upstream transport balanced by entrainment into richer conditions, while on the rich side, upstream turbulent transport and entrainment from leaner conditions balance the streamwise convection.