how old was lucie when her father was imprisoned?

Dr. Manette was imprisoned before Lucie was born.

“You speak collectedly, and you—are collected. That's good!” (Though his manner was less satisfied than his words.) “A matter of business. Regard it as a matter of business—business that must be done. Now if this doctor's wife, though a lady of great courage and spirit, had suffered so intensely from this cause before her little child was born—”
“The little child was a daughter, sir.”
“A daughter. A-a-matter of business—don't be distressed. Miss, if the poor lady had suffered so intensely before her little child was born, that she came to the determination of sparing the poor child the inheritance of any part of the agony she had known the pains of, by rearing her in the belief that her father was dead—No, don't kneel! In Heaven's name why should you kneel to me!”