Video-based lie detection aims to identify deceptive behaviors from visual cues. Despite recent progress, its core challenge lies in learning sparse yet discriminative representations. Deceptive signals are typically subtle and short-lived, easily overwhelmed by redundant information, while individual and contextual variations introduce strong identity-related noise. To address this issue, we propose GenLie, a Global-Enhanced Lie Detection Network that performs local feature modeling under global supervision. Specifically, sparse and subtle deceptive cues are captured at the local level, while global supervision and optimization ensure robust and discriminative representations by suppressing identity-related noise. Experiments on three public datasets, covering both high- and low-stakes scenarios, show that GenLie consistently outperforms state-of-the-art methods. Source code is available at https://github.com/AliasDictusZ1/GenLie.