A laboratory gas turbine model combustor with dual-swirler configuration is in- vestigated using Large Eddy Simulation (LES) with a flamelet subgrid combus- tion model. Two partially premixed methane/air flames with different equivalence ratio and thermal power are simulated: one stably burning with an elongated V- shape and another undergoing pronounced thermoacoustic oscillations exhibiting a flat shape. Additionally, both flames feature a hydrodynamic instability in the form of a precessing vortex core (PVC). Detailed comparisons between experi- mental and LES results show that the different flow and reaction zone structures in these two flames are reproduced well. The various flow dynamics resulting from the PVC and thermoacoustic oscillations are also captured accurately in the simulation. Further analyses on the lifted swirl flame stabilisation using phase averaged statistics at the PVC frequencies reveal that the PVC-induced stagnation points provide an anchoring mechanism for both the stable and unstable flames, although in the latter case large self-excited pressure oscillations are present. It is found that the PVC is significantly influenced by these oscillations, being axially stretched and compressed at high and low pressures, respectively. However, the formation of flame leading edge due to the PVC is robust during these unstable processes and the azimuthal movement of the leading point is found to be strongly correlated with the rotation of the PVC in both flames, further confirming the vital role of the PVC in the stabilisation process of these lifted swirl flames.