LoRA enables efficient customization of LLMs and is widely used in multi-tenant and multi-task serving. However, emerging model architectures such as MoE significantly increase LoRA memory cost, making existing coupled LoRA serving designs poorly scalable and prone to tail-latency inflation. We present InfiniLoRA, a disaggregated LoRA serving system that decouples LoRA execution from base-model inference. InfiniLoRA introduces a shared LoRA Server with parallelism-aware execution, SLO-driven provisioning, and critical-path optimizations, including GPU-initiated communication and hardware-specialized LoRA kernels. Experiments show that InfiniLoRA can achieve an average $3.05\times$ increase in serviceable request rate under strict latency SLOs, and improve the percentage of LoRA adapters satisfying the SLO requirement by 54.0\%.