High-quality 3D reconstruction of pulmonary segments plays a crucial role in segmentectomy and surgical planning for the treatment of lung cancer. Due to the resolution requirement of the target reconstruction, conventional deep learning-based methods often suffer from computational resource constraints or limited granularity. Conversely, implicit modeling is favored due to its computational efficiency and continuous representation at any resolution. We propose a neural implicit function-based method to learn a 3D surface to achieve anatomy-aware, precise pulmonary segment reconstruction, represented as a shape by deforming a learnable template. Additionally, we introduce two clinically relevant evaluation metrics to comprehensively assess the quality of the reconstruction. Furthermore, to address the lack of publicly available shape datasets for benchmarking reconstruction algorithms, we developed a shape dataset named Lung3D, which includes the 3D models of 800 labeled pulmonary segments and their corresponding airways, arteries, veins, and intersegmental veins. We demonstrate that the proposed approach outperforms existing methods, providing a new perspective for pulmonary segment reconstruction. Code and data will be available at https://github.com/HINTLab/ImPulSe.