A plethora of real-world scientific investigations is waiting to scale with the support of trustworthy predictive models that can reduce the need for costly data annotations. We focus on causal inferences on a target experiment with unlabeled factual outcomes, retrieved by a predictive model fine-tuned on a labeled similar experiment. First, we show that factual outcome estimation via Empirical Risk Minimization (ERM) may fail to yield valid causal inferences on the target population, even in a randomized controlled experiment and infinite training samples. Then, we propose to leverage the observed experimental settings during training to empower generalization to downstream interventional investigations, ``Causal Lifting'' the predictive model. We propose Deconfounded Empirical Risk Minimization (DERM), a new simple learning procedure minimizing the risk over a fictitious target population, preventing potential confounding effects. We validate our method on both synthetic and real-world scientific data. Notably, for the first time, we zero-shot generalize causal inferences on ISTAnt dataset (without annotation) by causal lifting a predictive model on our experiment variant.