The inherent flexibility and real-time deformation of breast tissue pose significant challenges for achieving full coverage and accurate lesion localization in autonomous breast ultrasound scanning. This paper introduces a robust finite state machine-based framework that mimics the decision-making process of an experienced physician, dynamically transitioning between the global breast scan and the fine lesion scan. An autonomous radial and anti-radial global scan pattern ensures comprehensive breast coverage. To avoid lesion misidentification caused by soft tissue movement, a real-time lesion fine scan method is proposed for lesion detection and localization. Experimental results demonstrate that the system in full coverage tests achieves 7 identified lesions out of 7 existing lesions and maintains a robust localization accuracy of$\mathbf{3. 2 3 ~ m m}$across phantoms with varying stiffnesses.