Continual learning in large language models (LLMs) typically encounters the critical challenge of catastrophic forgetting, where previously acquired knowledge deteriorates upon exposure to new data. While techniques like replay buffers and parameter-efficient tuning (e.g., Low-Rank Adaptation or LoRA) have been proposed, few studies investigate real-time domain adaptation under strict computational and data-stream constraints. In this paper, we demonstrate a lightweight method combining LoRA and a minimal replay mechanism in a realistic streaming setting across three diverse knowledge domains: medical question answering, genetics, and law. Using perplexity, semantic similarity, and GPT-based human-like evaluation metrics, we quantify the model's adaptation, forgetting, and recovery over time. Our experiments reveal that while catastrophic forgetting naturally occurs, even minimal replay significantly stabilizes and partially restores domain-specific knowledge. This study contributes practical insights for deploying adaptable LLMs in resource-constrained, real-world scenarios.