Length‑aware scheduling reduces LLM serving latency by prioritizing shorter requests, yet predictors often lose ranking quality under domain or task shifts and require costly retraining; their inference overhead can also erase scheduling gains. To improve generalization and efficiency, we introduce LEAP, a length‑prediction system with fast online adaptation and asynchronous CPU execution. LEAP reuses the serving model’s prefill hidden states, which already encode output‑length cues, and extracts them via a linear readout. When faced with substantial domain/task shifts, LEAP updates the readout at test time using recursive least squares, supervising on completed requests without gradient computation or replay of historical data. Prediction and updates run asynchronously on the CPU, overlapping the remaining GPU prefill. Across cross‑domain transfers, LEAP retains strong ranking ability and online adaptation boosts Spearman correlation by 64.7%. In serving experiments, LEAP cuts average per‑token latency by 15.9%–40.8%, raises throughput by 1.9%, and uses 30,569× fewer parameters than the strongest baseline.\n\nReview: LEAP’s clever reuse of internal model signals combined with lightweight online learning delivers efficient length prediction under constrained resources, offering a practical solution for real‑world deployment.