Literary translation is a difficult task that not only requires semantic accuracy but also stylistic richness and lexical diversity. Pretrained and supervised fine-tuned Large Language Models (LLMs) can over-rely on safe vocabulary choices, leading to translations that lack lexical variety. To address this problem, we propose a novel diversity-aware multi-objective Group Relative Policy Optimization (GRPO) framework that pushes the limits of open-source translation quality while increasing lexical diversity. We introduce two diversity-aware reward mechanisms, a Leave-One-Out (LOO) marginal contribution reward and a Self-BLEU penalty, balanced alongside neural quality metrics (COMET), lexical overlap (BLEU), and structural constraints. Through experiments on Turkish-English and German-English using Qwen3-14B, we show that our diversity-aware reinforcement learning approach successfully enhances lexical richness alongside translation quality. Our models achieve state-of-the-art open-source performance in literary translation, bridging the gap with leading commercial systems and demonstrating that policy optimization can effectively steer LLMs toward high-quality, lexically diverse outputs.