Lifelong Person Re-identification (LReID) suffers from a key challenge in preserving old knowledge while adapting to new information. The existing solutions include rehearsal-based and rehearsal-free methods to address this challenge. Rehearsal-based approaches rely on knowledge distillation, continuously accumulating forgetting during the distillation process. Rehearsal-free methods insufficiently learn the distribution of each domain, leading to forgetfulness over time. To solve these issues, we propose a novel Distribution-aware Forgetting Compensation (DAFC) model that explores cross-domain shared representation learning and domain-specific distribution integration without using old exemplars or knowledge distillation. We propose a Text-driven Prompt Aggregation (TPA) that utilizes text features to enrich prompt elements and guide the prompt model to learn fine-grained representations for each instance. This can enhance the differentiation of identity information and establish the foundation for domain distribution awareness. Then, Distribution-based Awareness and Integration (DAI) is designed to capture each domain-specific distribution by a dedicated expert network and adaptively consolidate them into a shared region in high-dimensional space. In this manner, DAI can consolidate and enhance cross-domain shared representation learning while alleviating catastrophic forgetting. Furthermore, we develop a Knowledge Consolidation Mechanism (KCM) that comprises instance-level discrimination and cross-domain consistency alignment strategies to facilitate model adaptive learning of new knowledge from the current domain and promote knowledge consolidation learning between acquired domain-specific distributions, respectively. Experimental results show that our DAFC outperforms state-of-the-art methods. Our code is available at https://github.com/LiuShiBen/DAFC.