A retention strategy based on an enlightened lapse modelization can be a powerful profitability lever for a life insurer. Some machine learning models are excellent at predicting lapse, but from the insurer's perspective, predicting which policyholder is likely to lapse is not enough to design a retention strategy. Changing the classical classification problem to a regression one with an appropriate validation metric based on Customer Lifetime Value (CLV) has recently been proposed. In our paper, we suggest several improvements and apply them to a sizeable real-world life insurance dataset. We include the risk of death in the study through competing risk considerations in parametric and tree-based models and show that further individualization of the existing approach leads to increased performance. We show that survival tree-based models with competing risk can outperform parametric approaches and that the actuarial literature can significantly benefit from them. Then, we compare how this framework leads to increased predicted gains for the insurer regardless of the retention strategy. Finally, we discuss the benefits of our modelization in terms of commercial and strategic decision-making for a life insurer.