Fine-tuning large language models (LLMs) for downstream tasks remains expensive, even with parameter-efficient methods like Low-Rank Adaptation (LoRA). In this regard, meta-learning approaches such as Model-Agnostic Meta-Learning for LLMs (MAML-en-LLM) and Amortized Bayesian Meta-Learning for LoRA (ABMLL) have emerged as promising solutions for rapid downstream LLM adaptation. However, these methods fundamentally couple two distinct objectives: learning generalizable initializations and enabling efficient task adaptation. We argue that this coupling limits both the quality of learned representations and adaptation efficiency. In this paper, we introduce **DeGAML-LLM** (**De**coupled **G**eneralization and **A**daptation in **M**eta-**L**earning for **LLM**s), a novel framework that explicitly separates these two objectives through dedicated parameter spaces. Specifically, we maintain a generalization module that learns task-agnostic representations across the task distribution, and an adaptation module that specializes in rapid task-specific adjustment. Extensive experiments on common-sense reasoning, mathematics, logic, social, medical and coding benchmarks across model scales demonstrate that DeGAML-LLM outperforms existing meta-learning and standard multi-task baselines.