Lung cancer is a leading cause of cancer-related deaths globally. PET-CT is crucial for imaging lung tumors, providing essential metabolic and anatomical information, while it faces challenges such as poor image quality, motion artifacts, and complex tumor morphology. Deep learning-based segmentation models are expected to address these problems, however, most existing datasets are small-scale and private, which is insufficient to support significant performance improvements for these methods. Hence, we introduce a large-scale PET-CT lung tumor segmentation dataset, termed PCLT20K, which comprises 21,930 pairs of PET-CT images from 605 patients. All images are manually labeled with pixel-level tumor masks by experienced doctors. Furthermore, we propose a cross-modal interactive perception network with Mamba (CIPA) for lung tumor segmentation in PET-CT images. Specifically, we design a channel-wise rectification module (CRM) that implements a channel state space block across multi-modal features to learn correlated representations and helps filter out modality-specific noise. A dynamic cross-modality interaction module (DCIM) is designed to effectively integrate position and context information, which employs PET images to learn regional position information and serves as a bridge to assist in modeling the relationships between local features of CT images. Extensive experiments on a comprehensive benchmark demonstrate the effectiveness of our CIPA compared to the current state-of-the-art segmentation methods. We hope our research can provide more exploration opportunities for medical image segmentation.