Why does adding salt to water help distillation?
Good question. We frequently "salt out" semi-soluble organic compounds from water because the ionic nature of the salt is more compatible with the water and less compatible with the (less ionic) organic compound. This is used, for instance, to drive sodium stearate (soap) from water. Adding salt could help drive more lanolin out of the water, or what is probably the situation, making an emulsion of water and lanolin less stable so that you can get more lanolin and less "grunge". The lanolin is then purified by filtering, which would remove salt crystals that formed as the water evaporated. And filtering would remove other dirt.

One description of obtaining lanolin suggests driving off all the water, then purifying by adding olive oil and water to remove dirt. But then it raises the question: why not remove the lanolin before all the water is evaporated? The salt would remain in the water. https://permies.com/t/65837/fiber-arts/extract-lanolin-wool

It's also possible that the water pulled out by the wool extracts a great deal of the salt, leaving the lanolin with only a small portion of the original salt and water (depending on how much water you use in the first place).