If a person on Shabbat needs drops to lubricate his eyes – such as for inserting contact lenses – he may use eyedrops for lubrication. This is the ruling of Hacham Ovadia Yosef, as cited in Yalkut Yosef (Shabbat, vol. 4, p. 110). Since this is not done for medical purposes, but simply to keep the eyes lubricated, it is permissible.
Hacham Ovadia permitted under certain circumstances the use on Shabbat of creams that are absorbed into the skin, despite the Shabbat prohibition of Memare’ah – smoothening a thick substance. This lenient ruling was based on the theory advanced by the Magen Abraham (Rav Abraham Gombiner, 1633-1683) that Memare’ah forbids smoothening a substance on a surface (such as applying wax to the cover of a barrel to seal it), but not when it is absorbed into the surface. Hacham Ovadia thus permitted the use of lotion for an infant’s rash, and for somebody suffering from a painful backache. However, the Mishna Berura Tiferet (328:76) notes that it is uncertain whether Hacham Ovadia would have also permitted applying hand cream to heal chapped skin on Shabbat. It is very possible that Hacham Ovadia allowed relying on the lenient position of the Magen Abraham only for the sake of a child, or in cases of severe pain. Therefore, it is proper to avoid the use of hand cream on Shabbat. By the same token, one should not use olive oil to treat chapped lips or chapped skin on Shabbat. Since olive oil is used on skin today exclusively for medicinal purposes, this would be forbidden on Shabbat due to the prohibition of Refu’a (taking medicine on Shabbat).
Summary: One who needs to lubricate his eyes on Shabbat (such as to insert contact lenses) may take lubricating eyedrops. Although it is permissible on Shabbat to apply lotion to an infant’s rash, and to use lotion in cases of considerable pain, it is proper to avoid using on Shabbat lotions or olive oil to treat chapped lips or chapped skin.