Why does lactose-free milk last so much longer than regular milk?
Apparently the process used by manufacturers (ultra-pasteurization) to produce lactose-free milk is responsible for the longer shelf life.

One source reports:


  Lactose-free milk is pasteurized at a higher temperature than regular milk. The process, known as ultra-pasteurization, is designed to remove the bacteria content entirely, giving lactose-free milk a refrigerated shelf-life of 60-90 days, compared with regular pasteurized milk, which retains some bacteria. It has a shelf life of 1-3 weeks.


A producer (in the United States) of organic dairy products (Organic Valley) describes ultra-pasteurization and the extended shelf-life here as:


  Ultra Pasteurization (UP), or Ultra High Temperature (UHT) pasteurization, is the process of heating milk to approximately  280 °F for just 2 seconds and then chilling it back down rapidly.  The result is milk that's 99.9% free from bacteria.  This pasteurization process creates an extended shelf-life for milk products of up to three times the length as HTST pasteurization; while providing the same wholesome, quality dairy product.  This allows us to distribute UP milk products regionally as well as to other areas of the country that might not have access to our dairy products. This is referred to as 'ultra pasteurized' on the milk package.  Organic Valley offers its quarts and some of its half gallons of milk with Ultra Pasteurization (UP).