Accurate workload forecasting is critical for elastic resource provisioning in web-scale cloud services, where distribution shifts driven by viral content, product launches, and user behavior degrade offline-trained models rapidly. Naive online learning recovers accuracy but incurs prohibitive per-step compute cost. We propose AdaptLSTM, an adaptive online framework that detects drift via validation-calibrated thresholds and applies selective, targeted updates. On the Alibaba Machine Trace, AdaptLSTM recovers 54\% of Naive Online's improvement at 20\% cost ($2.7\times$ efficiency, $p=0.002$ over 10 seeds). On the more volatile Container Trace, it achieves 96\% at 20\% cost ($4.8\times$ efficiency, $+75\%$ MAE reduction over Static). Unlike classical drift detectors (ADWIN, DDM, Page-Hinkley) which fail to trigger on regression-scale error streams, AdaptLSTM fires 42 times over 301 steps and outperforms matched-budget baselines. Wall-clock profiling shows $1.33\times$ throughput gain and 45\% update-time reduction. The framework is model-agnostic: identical Pareto patterns hold for LSTM, GRU, and Transformer backbones.

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