The commercialization of LLM applications is the next frontier in online advertising, with LLM-native advertising emerging as a promising paradigm by integrating ads into LLM-generated content. However, classic mechanisms are no longer applicable in this setting where the auction object is shifted from discrete ad slots to distributions over LLM outputs, and existing methods are impractical in industrial scenarios due to ignored externalities or high inference costs. To address these issues, we propose LLM-Auction, the first learning-based generative auction mechanism that integrates auction and generation. By formulating the allocation as preference alignment between LLM outputs and a mechanism objective that balances advertisers' value and user experience, we optimize the LLMs to inherently model allocation externalities without extra inference cost. Theoretically, we identify the allocation monotonicity and continuity of LLM-Auction, and prove that a simple first-price payment rule exhibits favorable incentive properties. Furthermore, we build an LLM-as-a-judge simulation environment for quantitative evaluation, and experiments demonstrate that LLM-Auction achieves the state-of-the-art allocation efficiency while satisfying key mechanism properties.