Graph Neural Networks (GNNs) have emerged as a fundamental tool for modeling complex graph structures across diverse applications. However, directly applying pretrained GNNs to varied downstream tasks without fine-tuning-based continual learning remains challenging, as this approach incurs high computational costs and hinders the development of Large Graph Models (LGMs). In this paper, we investigate an efficient and generalizable dataset distillation framework for Graph Continual Learning (GCL) across multiple downstream tasks, implemented through a novel Lightweight Graph Neural Tangent Kernel (LIGHTGNTK). Specifically, LIGHTGNTK employs a low-rank approximation of the Laplacian matrix via Bernoulli sampling and linear association within the GNTK. This design enables efficient capture of both structural and feature relationships while supporting gradient-based dataset distillation. Additionally, LIGHTGNTK incorporates a unified subgraph anchoring strategy, allowing it to handle graph-level, node-level, and edge-level tasks under diverse input structures. Comprehensive experiments on several datasets show that LIGHTGNTK achieves state-of-the-art performance in GCL scenarios, promoting the development of adaptive and scalable LGMs.