Spatio-temporal event forecasting, including emergency event prediction, traffic accident prediction, and mobility demand prediction, plays a vital role in resource allocation and public safety. However, existing prediction models can inadvertently amplify socioeconomic disparities through biased predictions that systematically favor advantaged communities. While recent fairness-aware approaches address global fairness across entire regions, they neglect local fairness that focuses on reducing disparities along the boundaries between neighborhoods with different socioeconomic statuses. We propose LG-Fair, a novel prediction framework that jointly optimizes both global and local fairness while maintaining prediction accuracy. Specifically, we propose novel local fairness metrics based on the corresponding global fairness counterparts for spatio-temporal forecasting. We design a flexible fairness framework that can optimize a hybrid loss function that balances prediction accuracy with fairness at both global and local scales. Our framework is generalizable as it can incorporate different fairness metrics and adapt to different backbone prediction architectures. Experiments on diverse real-world datasets demonstrate that LG-Fair significantly reduces fairness disparities at multiple spatial scales while maintaining competitive prediction performance, highlighting its potential in various application scenarios.