Low rank adaptation (LoRA) has emerged as a prominent technique for fine-tuning large language models (LLMs) thanks to its superb efficiency gains over previous methods. While extensive studies have examined the performance and structural properties of LoRA, its behavior upon training-time attacks remain underexplored, posing significant security risks. In this paper, we theoretically investigate the security implications of LoRA's low-rank structure during fine-tuning, in the context of its robustness against data poisoning and backdoor attacks. We propose an analytical framework that models LoRA's training dynamics, employs the neural tangent kernel to simplify the analysis of the training process, and applies information theory to establish connections between LoRA's low rank structure and its vulnerability against training-time attacks. Our analysis indicates that LoRA exhibits better robustness to backdoor attacks than full fine-tuning, while becomes more vulnerable to untargeted data poisoning due to its over-simplified information geometry. Extensive experimental evaluations have corroborated our theoretical findings.