Instructions
Lower your evil level. This is the simplest method of ensuring Lady Grey does not run away. Complete quests that raise your "Good" level, or just go to the Temple of Light and donate massive amounts of gold to the temple coffers. Either way will raise your goodness level and make it less likely that Lady Grey will try to take a powder when she sees you coming.
Obtain all the pieces of the Monk's Garb. Everyone trusts a monk, even if you're an evil chick-munching sociopath underneath the robes. Buy or find the Monk's Robe, the Monk's Gloves and the Monk's Shoes.
Wear the Monk Outfit when you go to see Lady Grey. Your pious appearance will soothe her fears, regardless of what you are like on the inside.
Wear clothing that grants a bonus to your attractiveness along with the Monk Outfit. You may have the clothes of a saint, but Lady Grey won't pay you any attention if you look like a slob. Put on clothes that grant a bonus to your attractiveness -- such as the Noble Gent's Shirt -- underneath your monk robes to make yourself more attractive to the zombie lady.