LiDAR-based 3D object detection models often struggle to generalize to real-world environments due to limited object diversity in existing datasets. To tackle it, we introduce the first generalized cross-domain few-shot (GCFS) task in 3D object detection, aiming to adapt a source-pretrained model to both common and novel classes in a new domain with only few-shot annotations. We propose a unified framework that learns stable target semantics under limited supervision by bridging 2D open-set semantics with 3D spatial reasoning. Specifically, an image-guided multi-modal fusion module injects transferable 2D semantic cues into the 3D detection pipeline via vision-language models, while a physically-aware box search enhances 2D-to-3D alignment via LiDAR priors. To capture class-specific semantics from sparse data, we further introduce contrastive-enhanced prototype learning, which encodes few-shot instances into discriminative semantic anchors and stabilizes representation learning. Extensive experiments on four GCFS benchmarks demonstrate the effectiveness and generality of our approach in realistic deployment settings. The code will be publicly available.