Estring, a vaginal ring, is one method for delivering localized hormones—in this case estradiol. The ring itself includes silicone polymers, so I recommend to my patients that they use a water-based or hybrid lubricant. Among water-based lubricants, Yes and Aloe Cadabra are often ordered. ID Silk is popular among post-menopausal women; as a hybrid lubricant, it has the benefits of water-based but is more long lasting, like silicone-based.
Silicone-based lubricants aren't recommended for use with products made from silicone—like the Estring and some vibrators or other sex toys—because the formula may cause disintegration of the surface.