Partial fuel stratification (PFS) is a promising fuel injection strategy to stabilize lean premixed combustion in spark-ignition (SI) engines. PFS creates a locally stratified mixture by injecting a fraction of the fuel, just before spark timing, into the engine cylinder containing homogeneous lean fuel/air mixture. This locally stratified mixture, when ignited, results in complex flame structure and propagation modes similar to partially premixed flames, and allows for faster and more stable flame propagation than a homogeneous lean mixture. This study focuses on understanding the detailed flame structures associated with PFS-assisted lean premixed combustion. First, a two-dimensional direct numerical simulation (DNS) is performed using detailed fuel chemistry, experimental pressure trace, and realistic initial conditions mapped from a prior engine large-eddy simulation (LES), replicating practical lean SI operating conditions. DNS results suggest that conventional triple flame structures are prevalent during the initial stage of flame kernel growth. Both premixed and non-premixed combustion modes are present with the premixed mode contributing dominantly to the total heat release. Detailed analysis reveals the effects of flame stretch and fuel pyrolysis on the flame displacement speed. Based on the DNS findings, the accuracy of a hybrid G-equation/well-stirred reactor (WSR) combustion model is assessed for PFS-assisted lean operation in the LES context. The G-equation model qualitatively captures the premixed branches of the triple flame, while the WSR model predicts the non-premixed branch of the triple flame. Finally, potential needs for improvements to the hybrid G-equation/WSR modeling approach are discussed.