According to Breastfeeding Medicine (May 2019) oxidation--not high levels of lipase-- in the milk is the cause of off odors in breasmilk. Although Lipase is present to help break down the fat molecules, it doesn't increase in levels in off-odor milk. Testing of off-smelling breastmilk was determined to be exposure of free fatty acids, but no increase in lipase was found in the stronger smelling human milk vs. the more mildly smelling human milk. Oxidation seemed to be the culprit that causes these off odors in stored milk especially those that indicate rancidity.

The recommendation to reduce off-odors is to reduce the oxidation potential in storing human milk in the fridge or freezer. Fill the bags or bottles as full as possible to reduce the risk, seal the containers well, and of course use the freshest milk possible for babies for the most bio-available components (including IgA) as longer time in the freezer will destroy some of the cellular activity and vitamins.