In air-ground collaboration scenarios without GPS and prior maps, the relative positioning of drones and unmanned ground vehicles (UGVs) has always been a challenge. For a drone equipped with monocular camera and an UGV equipped with LiDAR as an external sensor, we propose a robust and real-time relative pose estimation method (LVCP) based on the tight coupling of vision and LiDAR point cloud information, which does not require prior information such as maps or precise initial poses. Given that large-scale point clouds generated by 3D sensors has more accurate spatial geometric information than the feature point cloud generated by image, we utilize LiDAR point clouds to correct the drift in visual-inertial odometry (VIO) when the camera undergoes significant shaking or the IMU has a low signal-to-noise ratio. To achieve this, we propose a novel coarse-to-fine framework for LiDAR-vision collaborative localization. In this framework, we construct point-plane association based on spatial geometric information, and innovatively construct a point-aided Bundle Adjustment (BA) problem as the backend to simultaneously estimate the relative pose of the camera and LiDAR and correct the VIO drift. In this process, we propose a particle swarm optimization (PSO) based sampling algorithm to complete the coarse estimation of the current camera-LiDAR pose. In this process, the initial pose of the camera used for sampling is obtained based on VIO propagation, and the valid feature-plane association number (VFPN) is used to trigger PSO-sampling process. Additionally, we propose a method that combines Structure from Motion (SFM) and multi-level sampling to initialize the algorithm, addressing the challenge of lacking initial values.