Accurate breast ultrasound (BUS) lesion segmentation is critical for early diagnosis but is challenged by image artifacts and the reliance of foundation models on manual prompting. Existing automated frameworks often lack robust fail-safe mechanisms, leading to missed diagnoses. To address this reliability gap, this study proposes a novel, fully automated hybrid segmentation framework that synergistically integrates three key components: (1) a recall-optimized YOLOv9 detector tailored to minimize clinical false negatives; (2) a MedSAM2 foundation model efficiently fine-tuned via Low-Rank Adaptation (LoRA) for ultrasound specifics; and (3) a statistical fallback mechanism that acts as a crucial safety net to recover spatial prompts during detection failures. Evaluated on the public BUSI dataset, the recall-dominant detection module achieved a Recall of 0.8238. Supported by this robust prompting and fallback strategy, the segmentation module achieved a Dice coefficient of 0.8818 and an IoU of 0.8113. By effectively integrating specialized detection with adaptive segmentation and a statistical fail-safe, the proposed pipeline offers a highly reliable automated approach for computer-aided screening systems.