Recommendation systems play a vital role in many online platforms, with their primary objective being to satisfy and retain users. As directly optimizing user retention is challenging, multiple evaluation metrics are often employed. Existing methods generally formulate the optimization of these evaluation metrics as a multitask learning problem, but often overlook the fact that user preferences for different tasks are personalized and change over time. Identifying and tracking the evolution of user preferences can lead to better user retention. To address this issue, we introduce the concept of "user lifecycle", consisting of multiple stages characterized by users' varying preferences for different tasks. We propose a novel Stage-Adaptive Network (STAN) framework for modeling user lifecycle stages. STAN first identifies latent user lifecycle stages based on learned user preferences, and then employs the stage representation to enhance multi-task learning performance. Our experimental results using both public and industrial datasets demonstrate that the proposed model significantly improves multi-task prediction performance compared to state-of-the-art methods, highlighting the importance of considering user lifecycle stages in recommendation systems. Furthermore, online A/B testing reveals that our model outperforms the existing model, achieving a significant improvement of 3.05% in staytime per user and 0.88% in CVR. These results indicate that our approach effectively improves the overall efficiency of the multi-task recommendation system.