Large Language Models (LLMs) have demonstrated remarkable generalization across diverse NLP tasks, yet they often produce outputs lacking semantic coherence due to insufficient grounding in structured linguistic knowledge. This paper proposes a novel method for injecting Frame Semantics into a pretrained LLaMA model using Low-Rank Adaptation (LoRA). Leveraging FrameNet (a rich resource of over 1,000 semantic frames) we construct a training corpus comprising structured triples of frame definitions, frame elements, and lexical units. Our method encodes these examples into the model via LoRA adapters and evaluates performance using zero-shot prompting for textual entailment and semantic role labeling (SRL) over Framenet. Experimental results show that our adapted frame-aware LLM substantially outperforms the baseline across closed, open-ended, and multiple-choice prompts. Moreover, we observe significant improvements in SRL accuracy, demonstrating the efficacy of combining frame-semantic theory with parameter-efficient pretraining.