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This paper investigates the role of dynamic external knowledge integration in improving counter-argument generation using Large Language Models (LLMs). While LLMs have shown promise in argumentative tasks, their tendency to generate lengthy, potentially non-factual responses highlights the need for more controlled and evidence-based approaches. We introduce a reconstructed and manually curated dataset of argument and counter-argument pairs specifically designed to balance argumentative complexity with evaluative feasibility. We also propose a new LLM-as-a-Judge evaluation methodology that shows a stronger correlation with human judgments compared to traditional reference-based metrics. Our experimental results demonstrate that integrating dynamic external knowledge from the web significantly improves the quality of generated counter-arguments, particularly in terms of relatedness, persuasiveness, and factuality. The findings suggest that combining LLMs with real-time external knowledge retrieval offers a promising direction for developing more effective and reliable counter-argumentation systems. Data and code are publicly available: https://github.com/anaryegen/ counter-argument-generation