Lean premixed gas turbulent flames stabilized in the flow generated by an industrial swirl burner with a central bluff body are experimentally found to behave bi-stable. This bi-stable behaviour, which can be triggered via a small change in some of the controlling parameters, for example the bulk equivalence ratio, consists in a rather sudden transition of the flame from completely lifted to well attached to the bluff body. While several experimental investigations exist on this topic, numerical analysis is limited. The present work is therefore also of numerical nature, with a two-fold scope: a) simulation and validation with experiments of the bi-stable flame behaviour via Computational Fluid Dynamics (CFD) in the form of Large Eddy Simulation (LES) and b) analysis of CFD results to shed light on the flame stabilization properties. LES results, in case of the lifted flame, show that the vortex core is sharply precessing at a given frequency. Phase averaging these results at the frequency of precession clearly indicates a counter-intuitive and unexpected presence of reverse flow going all the way through the flame apex and the bluff body tip. A simple one-dimensional flame stabilization model is applied to explain the bi-stable flame behaviour.