Context retrieval systems for LLM inference face a critical challenge: high retrieval latency creates a fundamental tension between waiting for complete context (poor time-to-first-token) and proceeding without it (reduced quality). Streaming context incrementally--overlapping retrieval with inference--can mitigate this latency, but doing so with concurrent requests introduces new challenges: requests contend for GPU compute and memory, and scheduling must adapt to dynamic context arrivals. We present Stream2LLM, a streaming-aware LLM serving system for concurrent prefill-decode disaggregated deployments. Stream2LLM introduces adaptive scheduling and preemption for two distinct retrieval patterns: append-mode (progressive context accumulation) and update-mode (iterative refinement with cache invalidation). It decouples scheduling decisions from resource acquisition, enabling flexible preemption strategies guided by hardware-specific cost models, and uses longest common prefix matching to minimize redundant computation when input changes dynamically. To evaluate Stream2LLM, we collect two large-scale, real-world streaming workloads based on web crawling and approximate nearest neighbor search. Our evaluation demonstrates that streaming architecture delivers up to 11x TTFT improvements, with cost-aware scheduling providing critical benefits under memory pressure, all while maintaining throughput parity with non-streaming baselines. Code: https://github.com/rajveerb/stream2llm/tree/mlsys_artifact