It appears that "The Golden Thread" refers to Lucie - there is a direct quote that compares her blond hair to "the golden thread that bound them all together", but likewise it appears to point towards a larger symbolism and opposition of light vs darkness that is apparent in the novel, especially in the characters of Lucie and Madame Defarge. Also, it is perhaps highly significant that at the very end of the novel we are told of Lucie and Charles' son, who bears the name Sidney, and has golden hair:
I see that child who lay upon her bosom and who bore my name, a man winning his way up in that path of life which once was mine. I see him winning it so well, that my name is made illustrious there by the light of his... bringing a boy of my name, with a forehead that I know and golden hair, to this place -
The Golden Thread then perhaps symbolises the hope of new life, of happiness and of joy that can seem so thin and delicate in the face of overwhelming darkness, such as the French Revolution.