Know that "lot" is not an acronym, it is a word meaning "an item or set of items for sale" (and also in American English "a plot of land", but that is also an artefact of how land is/was sold). So as others have said, a lot number will be concerning the sale of goods, whereas a batch number is concerning how the manufacture of those goods is arranged.
It may well be that a lot consists of multiple batches, or that a batch is divided into multiple lots. Two distributors may have the same product with different lot numbers because the product was ordered and sold specifically for each distributor alone.