The process of digestion works a bit differently. When you put lime juice in milk, it curdles. That's because you are establishing a direct contact between lime and acid which gives rise to chemical reactions. In case of digestion, the milk undergoes many other processes before coming in contact with Sulphuric acid. The milk is acted upon by pepsin, an enzyme that breaks the protein in milk. Then lactase enzyme begins to break down lactic acid. After that the carbohydrates and fats are broken down. So it is a step by step process and not an all of a sudden process. Which is why milk doesn't curdle during digestion.
Hope this helped.