This paper studies the flame dynamics near lean blowout (LBO) conditions in a stratified swirl burner. The novel BASIS burner is used and fueled with premixed methane/air mixture at atmospheric conditions. In the experiments, only the pilot flame works with four different equivalent ratios. It is found that as the flame changes from stable combustion to near LBO, the flame macrostructure changes from V-shape to M-shape. Meanwhile, a characteristic frequency of 405 Hz is found in the spectrum of heat release signal. The closer to LBO, the higher amplitude is found at the frequency peak. Post-processing of flame images illustrates that the 405 Hz comes from the circumferential movement of the flame. Large-eddy simulations (LESs) via OpenFOAM reproduce the flame dynamics near LBO, which agrees with the experimental results. LESs provide more insights into the flow fields, showing that the characteristic frequency of 405 Hz comes from the flame-vortex interaction. This study reveals the mechanism of flame and vortex interactions in a stratified swirl burner near LBO. The heat release signal is also found can be used as a candidate precursor for LBO.