High-quality multispectral LiDAR (MSL) data are crucial for land cover (LC) classification. However, the Titan MSL system encounters challenges of inconsistent spatial–spectral information due to its unique scanning and data saving method, restricting subsequent classification accuracy. Existing spectral reconstruction methods often require empirical parameter settings and involve high computational costs, limiting automation and complicating application. To address this problem, we introduce the dual attention spectral optimization reconstruction network (DossaNet), leveraging an attention mechanism and spatial–spectral information. DossaNet can adaptively adjust weight parameters, streamline the multispectral point cloud acquisition process, and integrate it into classification models end-to-end. The experimental results show the following: (1) DossaNet exhibits excellent generalizability, effectively recovering accurate LC spectra and improving classification accuracy. Metrics across the six classification models show some improvements. (2) Compared with the method lacking spectral reconstruction, DossaNet can improve the overall accuracy (OA) and average accuracy (AA) of PointNet++ and RandLA-Net by a maximum of 4.8%, 4.47%, 5.93%, and 2.32%. Compared with the inverse distance weighted (IDW) and k-nearest neighbor (KNN) approach, DossaNet can improve the OA and AA of PointNet++ and DGCNN by a maximum of 1.33%, 2.32%, 0.86%, and 2.08% (IDW) and 1.73%, 3.58%, 0.28%, and 2.93% (KNN). The findings further validate the effectiveness of our proposed method. This method provides a more efficient and simplified approach to enhancing the quality of multispectral point cloud data.