The use of lifted flames presents some very promising advantages in terms of pollutant emissions and flame stability. The focus here is on a specific low-swirl injection system operated with methane and derived from an air-blast atomizer for aero-engine applications, which is responsible for flame lift-off. The key feature of this concept is the interaction between the swirling jet and the confinement walls, leading to a strong outer recirculation zone and thus to an upstream transport of combustion products from the main reaction region to the flame base. Here, the representation of the physics involved is challenging, since finite-rate effects govern the lift-off occurrence, and only a few numerical studies have been carried out on this test case so far. The aim of the present work is therefore to understand the limits of some state-of-the-art combustion models within the context of LES. Considering this context, two different strategies are adopted: the Flamelet-Generated Manifold (FGM) approach and the Thickened Flame (TF) model. A modified version of the FGM model including stretch and heat loss effects is also applied as an improvement of the standard model. Numerical results are compared with the available experimental data in terms of temperature and chemical species concentration maps, showing that the TF model can better reproduce the lift-off than the FGM approach.