Deep learning-based machine listening is broadening the scope of industrial acoustic analysis, yet its widespread implementation on live shop floors is hindered by the reliance on large, task-specific annotated datasets for every new task. While emerging general-purpose sound foundation models aim to alleviate data dependency, they reveal critical dilemmas in practice. General-purpose sound foundation models are computationally expensive and fail in industrial scenarios characterized by tonal harmonics, broadband noise, and transient fault events, making instant, on-site deployment impractical. These challenges combined mean that a practical, end-to-end system for deploying a sound foundation model on a live shop floor has remained elusive. To address this challenge, this study introduces LISTEN (Lightweight Industrial Sound-representable Transformer for Edge Notification), the first lightweight foundation model specialized for industrial sound. Through Knowledge Distillation (KD) from the large-scale teacher model IMPACT (Industrial Machine Perception via Acoustic Cognitive Transformer), we construct LISTEN optimized for resource-constrained edge environments. By freezing the backbone and training only a shallow head on minimal target-process data, rather than performing full fine-tuning or retraining, LISTEN achieves nearly identical performance to IMPACT across diverse manufacturing processes. This study further demonstrates a complete system for real-time machine monitoring, encompassing data acquisition with Industrial Internet of Things (IIoT) devices, rapid model adaptation using minimal annotated data, and real-time monitoring on a low-cost edge device. By validating the entire system on a live CNC machine, this work establishes the first feasible end-to-end system for deploying a lightweight industrial sound foundation model in an active industrial environment.