The lean burn combustion concept has shown potential for a further reduction of pollutants from aero engines. Partially premixed swirled flames in lean burn combustors strongly influence stability, performance and pollutant emissions associated with this concept and remain a major challenge when it comes to their prediction by numerical simulations. Large-Eddy Simulations (LES) for non-reactive and chemically reactive two-phase flows are performed for the DLR Generic Single Sector Combustor, which is a generic spray burner typical for lean burn combustors. Most simulations published on this kerosene burner do not accurately capture the lift-off height of the flame and the temperature distributions within the flow field. In contrast to previous scale-resolving simulations, the focus of this work is on LES, employing Finite-Rate Chemistry (FRC) for detailed combustion modeling. A reaction mechanism with 59 species and 372 elementary reactions and an Assumed Probability Density Function (APDF) approach for turbulence-chemistry interaction is used. The non-reacting mean velocity field, the spray distribution, flame shape, and flame lift-off height obtained from the simulations agree well with experimental data. In the flame, both premixed and diffusion-dominated regions are identified. Premixed zones occur predominantely, mainly as coherent structures in areas with high temperature gradients, whereas diffusion-dominated flame zones occur as isolated regions. For the detailed analysis of the burner, the employed numerical framework, including FRC, was found to be essential for an accurate prediction of the complex flame structure.