Recommender systems have been widely used in e-commerce, and re-ranking models are playing an increasingly significant role in the domain, which leverages the inter-item influence and determines the final recommendation lists. Online learning methods keep updating a deployed model with the latest available samples to capture the shifting of the underlying data distribution in e-commerce. However, they depend on the availability of real user feedback, which may be delayed by hours or even days, such as item purchases, leading to a lag in model enhancement. In this paper, we propose a novel extension of online learning methods for re-ranking modeling, which we term LAST, an acronym for Learning At Serving Time. It circumvents the requirement of user feedback by using a surrogate model to provide the instructional signal needed to steer model improvement. Upon receiving an online request, LAST finds and applies a model modification on the fly before generating a recommendation result for the request. The modification is request-specific and transient. It means the modification is tailored to and only to the current request to capture the specific context of the request. After a request, the modification is discarded, which helps to prevent error propagation and stabilizes the online learning procedure since the predictions of the surrogate model may be inaccurate. Most importantly, as a complement to feedback-based online learning methods, LAST can be seamlessly integrated into existing online learning systems to create a more adaptive and responsive recommendation experience. Comprehensive experiments, both offline and online, affirm that LAST outperforms state-of-the-art re-ranking models.