As label noise, one of the most popular distribution shifts, severely degrades deep neural networks' generalization performance, robust training with noisy labels is becoming an important task in modern deep learning. In this paper, we propose our framework, coined as Adaptive LAbel smoothing on Sub-ClAssifier (ALASCA), that provides a robust feature extractor with theoretical guarantee and negligible additional computation. First, we derive that the label smoothing (LS) incurs implicit Lipschitz regularization (LR). Furthermore, based on these derivations, we apply the adaptive LS (ALS) on sub-classifiers architectures for the practical application of adaptive LR on intermediate layers. We conduct extensive experiments for ALASCA and combine it with previous noise-robust methods on several datasets and show our framework consistently outperforms corresponding baselines.