Why does lady Macbeth fail to answer Duncan's inquiry as to the whereabouts of the Thane of Cawdor in Act I, scene 6?
Although we don't know exactly where Macbeth actually is when Duncan arrives at Inverness and is greeted by Lady Macbeth, perhaps her avoidance of the king's question is based on her husband's behavior at the end of scene 5. She doesn't trust Macbeth to be in Duncan's presence yet because she fears Macbeth may betray their as-yet fragile murder plot merely by the expression on his face. She had only a brief time to speak with her husband upon his arrival at Inverness.
In 1.5 she warns him that his face "is as a book where men/May read strange matters." Then she instructs him to "Look like the innocent flower,/But be the serpent under 't." Macbeth's response to her encouragement indicates he hasn't made up his mind: "We will speak further" (1.5.83). He simply isn't convinced yet that killing Duncan is an option.
On the other hand, Macbeth may simply be recovering from the journey by cleaning up and resting. After all, he arrives just before Duncan and his entourage.
The King's question is more of an introduction and of a rhetorical nature than a direct inquiry. He uses it to lead into the fact that Macbeth rode quickly to get home to this lovely house and wife, in which he and his court are guests this evening. The irony is that Duncan speaks affectionately and of Macbeth's love for his wife, completely unaware of what Lady Macbeth has up her sleeve. She answers him that she is glad he is a guest in her house, and he should treat her house as his own house as she says they are all "his servants".
The King then takes her arm and asks her to lead him to Macbeth so he can continue to honor the great deeds Macbeth has done for Duncan and Scotland.