Event cameras are bio-inspired sensors with some notable features, including high dynamic range and low latency, which makes them exceptionally suitable for perception in challenging scenarios such as high-speed motion and extreme lighting conditions. In this paper, we explore their potential for localization within pre-existing LiDAR maps, a critical task for applications that require precise navigation and mobile manipulation. Our framework follows a paradigm based on the refinement of an initial pose. Specifically, we first project LiDAR points into 2D space based on a rough initial pose to obtain depth maps, and then employ an optical flow estimation network to align events with LiDAR points in 2D space, followed by camera pose estimation using a PnP solver. To enhance geometric consistency between these two inherently different modalities, we develop a novel frame-based event representation that improves structural clarity. Additionally, given the varying degrees of bias observed in the ground truth poses, we design a module that predicts an auxiliary variable as a regularization term to mitigate the impact of this bias on network convergence. Experimental results on several public datasets demonstrate the effectiveness of our proposed method. To facilitate future research, both the code and the pre-trained models are made available online.