Large language model-based Recommender Systems (LRSs) have demonstrated superior recommendation performance by integrating pre-training with Supervised Fine-Tuning (SFT). However, this approach introduces item-side unfairness. Existing studies primarily attribute this issue to the absence of fairness constraints during SFT and attempt to mitigate unfairness via re-weighting and re-ranking methods. In this paper, we find that unfairness arises not only from SFT but also from pre-training, where inherent biases are further amplified during SFT. This finding underscores the failure of current methods to address the root causes of unfairness. Moreover, current methods struggle to preserve satisfactory recommendation performance. To tackle these issues, we propose an Unfair-to-Fair evOlving (UFO) framework using a self-play mechanism, formulating unfairness mitigation as a two-player game. UFO alternates between two player roles: the \textit{judger}, which identifies unfairness from both pre-training and SFT, and the \textit{corrector}, which adjusts the LRS to address identified unfairness while preserving recommendation performance. Iterative optimization between these roles enables UFO to completely resolve unfairness. Extensive experiments demonstrate that UFO effectively mitigates unfairness while improving recommendation performance.