Vision-language models achieve expert-level performance on medical imaging tasks but exhibit significant diagnostic accuracy disparities across demographic groups. We introduce fairness-aware Low-Rank Adaptation for medical VLMs, combining parameter efficiency with explicit fairness optimization. Our key algorithmic contribution is a differentiable MaxAccGap loss that enables end-to-end optimization of accuracy parity across demographic groups. We propose three methods: FR-LoRA integrates MaxAccGap regularization into the training objective, GR-LoRA applies inverse frequency weighting to balance gradient contributions, and Hybrid-LoRA combines both mechanisms. Evaluated on 10,000 glaucoma fundus images, GR-LoRA reduces diagnostic accuracy disparities by 69% while maintaining 53.15% overall accuracy. Ablation studies reveal that strong regularization strength achieves optimal fairness with minimal accuracy trade-off, and race-specific optimization yields 60% disparity reduction. Our approach requires only 0.24% trainable parameters, enabling practical deployment of fair medical AI in resource-constrained healthcare settings.