The "Golden Thread" refers to the character of Lucie Manette, who becomes Lucie Darnay after her marriage to Charles Darnay.
"The Golden Thread" is a good title for Book the Second because Lucie is the thread which unifies the narrative and binds the main characters together. Although she herself is largely passive, she is the object of devotion for her father Dr. Manette, Charles Darnay, and Sidney Carton. Through the inspiration of her gentleness and loving nature, all three characters are transformed.
Lucie, symbolic of light and goodness, has golden hair. Like the light, which also might be described as golden, she illuminates the lives of those around her. She tenderly nurses her father, who, after having been confined in solitary for eighteen years in prison, has lost touch with the world and is little more than a shadow, existing in a place in his mind far removed from reality. Through Lucie's love, he is "called to life" once again, and is able to regain a tangible but tenuous hold in the real world. Charles Darnay falls in love with Lucie at his first trial, and eventually marries her, with the permission of the good Doctor, her father. And Sydney Carton, the degenerate soul who loves Lucie as well but knows he cannot attain her, nevertheless entreats her to retain him as a friend. Eventually, her goodness inspires him to an ultimate act of honor and nobility, when he courageously gives up his very life so that she might be happy.
As it is so aptly stated in Enotes at the second link referenced below,
"Lucie is a catalyst. She does not change anything herself, but she is the cause of change in others".
Lucie is a major influence of the major characters in Book the Second; in her goodness she is the golden thread that binds their lives together.