Customer lifetime value (LTV) is crucial to companies who are intending to adopt personalized promoting strategies to optimize the profits. However, LTV prediction in the scenario of online App advertising usually suffers from label sparsity issue, towards which existing methods designed complex model structures but ignored the information contained in intermediate user behaviors. Moreover, previous works mainly focus on fitting the overall LTV distribution, overlooking the fact that LTV in online App advertising consists of sources with diverse data distributions and thus resulting in sub-optimal solutions. In this paper, we propose a novel Progressive Tasks guided Multi-Source Network (PTMSN) to tackle the aforementioned problems. Specifically, a Cascaded Sub-task Module (CSM) is introduced to alleviate data sparsity by modeling reliance between explicit interactions and implicit monetization. In addition, as the overall LTV is assembled from multiple sources, we propose a divide-and-conquer scheme named Multi-source Integrating Module (MIM) to disentangle the original single target into several source distributions and model in a fine-grained manner. Extensive offline experiments on real-world industrial datasets compared to state-of-the-art baseline models validate the effectiveness of our approach. PTMSN has been successfully deployed in industrial online advertising system, serving various business scenarios and acquiring 2.97% absolute ROI gains.