Lather is essential for natural soaps ability to wash dirt away, but chemical detergents don't really need lather, it is in there because people have associated lather with being clean. Look at solvents, like acetone, mineral spirits and so on. They are great cleaners, but it has nothing to do with lather. Certain soaps lather better than other because of the type of oils used. Coconut oil is a popular oil to turn into soap specifically because it creates a rich lather. Has something to do with the fatty acids present in the oil during the soap making process.