What is Lucie's "thread"? She represents the golden thread, but what is the actual thread in A Tale of Two Cities?
The "thread" is a golden hair from Lucie's head that matches the golden hair which Dr. Manette has kept in a little rag around his neck during his eighteen-year imprisonment. It acts as a metaphorical thread to sew together his tragic past and delusions with his memories.
This "thread" of Lucie's connects the present with the past--sews time together, as it were. For, upon seeing it, Dr. Manette realizes Lucie's hair must somehow belong to the other hairs that he has kept for so long. The thread brings back some of Manette's memory:
He took her hair into his hand again, and looked closely at it. "It is the same. How can it be! When was it! How was it!"
Then Dr. Manette relates how his lovely wife laid her head on his shoulders, fearing his departure so long ago, though he had no apprehensions. But, she was, of course, right. When Manette was incarcerated in the North Tower of the Bastille, the jailers found the long golden hairs on him. So, Manette requested that he be allowed to keep them, saying that they would help him escape in spirit, at least.
As he sits staring at her hair, Lucie comforts him and tells him that at another time her name will be revealed. She holds him and lies on the floor with him when he collapses, comforting the poor man. But, she does not yet reveal that she is his daughter.