This large eddy simulation (LES) study is applied to three different premixed turbulent flames under lean conditions at atmospheric pressure. The hierarchy of complexity of these flames in ascending order are a simple Bunsen-like burner, a suddenexpansion dump combustor, and a typical swirl-stabilized gas turbine burner-combustor. The purpose of this paper is to examine numerically whether the chosen combination of the Smagorinsky turbulence model for sgs fluxes and a novel turbulent premixed reaction closure is applicable over all the three combustion configurations with varied degree of flow and turbulence. A quality assessment method for the LES calculations is applied. The cold flow data obtained with the Smagorinsky closure on the dump combustor are in close proximity with the experiments. It moderately predicts the vortex breakdown and bubble shape, which control the flame position on the double-cone burner. Here, the jet break-up at the root of the burner is premature and differs with the experiments by as much as half the burner exit diameter, attributing the discrepancy to poor grid resolution. With the first two combustion configurations, the applied subgrid reaction model is in good correspondence with the experiments. For the third case, a complex swirl-stabilized burner-combustor configuration, although the flow field inside the burner is only modestly numerically explored, the level of flame stabilization at the junction of the burner-combustor has been rather well captured. Furthermore, the critical flame drift from the combustor into the burner was possible to capture in the LES context (which was not possible with the RANS plus k-ɛ model), however, requiring tuning of a prefactor in the reaction closure.