In-Context Reinforcement Learning (ICRL) is a frontier paradigm to solve Reinforcement Learning (RL) problems in the foundation-model era. While ICRL capabilities have been demonstrated in transformers through task-specific training, the potential of large language models (LLMs) out of the box remains largely unexplored. This paper investigates whether LLMs can generalize cross-domain to perform ICRL on the Dueling Bandits (DB) problem, a stateless preference-based RL setting. We find that top-performing LLMs exhibit a notable zero-shot capacity for relative decision-making, which translates to low short-term weak regret across all DB environments by quickly including the best arm in duels. However, an optimality gap still exists between LLMs and classic DB algorithms in terms of strong regret. LLMs struggle to converge and consistently exploit even when explicitly prompted to do so, and they are sensitive to prompt variations. To bridge this gap, we propose an agentic-flow framework—LLM with Enhanced Algorithmic Dueling (LEAD)—which integrates off-the-shelf DB algorithm support with LLM agents through fine-grained adaptive interplay. We show that LEAD inherits theoretical guarantees from classic DB algorithms on both weak and strong regret. We validate its efficacy and robustness even with noisy and adversarial prompts. The design of such an agentic framework sheds light on how to enhance the trustworthiness of general-purpose LLMs generalized to in-context decision-making tasks.