- "The Clanks are enforcing a curfew."
- "Really? It will be like old times then. We'd better change. You get to packing."
- Agatha and Lilith Clay
Judy, along with her husband, Punch, is one of the earliest construct creations of the Heterodyne Boys. As an early creation, she shows signs of being 'student work'; for example, one of her eyes used to be bigger than the other, something she disguised with special glasses. It is perhaps those flaws that helped disguise her and Punch in later years, for while some might see that she was a construct, they could not accept that this 'imperfect' work was the product of the legendary Heterodyne Boys. Her skillset includes playing the piano, canning foods, casing the thieves' market, being a good foster mom, and infiltrating floating castles.
She and Punch spent many years adventuring with the Heterodyne Boys, and it is through stories of these adventures that much of Europa remember them both. Unfortunately, they are both portrayed as goofy sidekicks in most Heterodyne Plays. 
For many years she passed herself off as a normal human, going by the name of Lilith Clay, and (along with Punch) raised Agatha (and gave piano lessons)while awaiting Barry's return. She and Punch were torn apart by Von Pinn while rescuing Agatha from Castle Wulfenbach, but both of them were reassembled in secret by Gilgamesh Wulfenbach.. Gil not only restored them, but also improved on their original construction, allowing Punch to speak where he was previously mute; adjusting Judy's eyes so that they are the same size, and allowing Punch and Judy to (unexpectedly) have their biological daughter, Maxinia Agatha Gilliana Heterodyne Clay. 
Time Skip (Approximately two and a half years after Bomb/Door)
Lilith sees to the small number of children hidden in the Sneaky Heterodyne cave. Time froze for Mechanicsburg, but the rest of the world still turned. Having not left for other towns presumably means these children are related to Mechanicsburg citizens or returning emigres.
Outside information and speculation
When Punch and Judy kept Agatha in hiding with them as their child, they went by the aliases Adam and Lilith Clay. Adam was the name given to the first man in the Bible, and some myths refer to Lilith as the wife of Adam prior to Eve. Given that some creation accounts refer to humans being fashioned from clay, and that the medieval story of the Golem also refers to its being made from clay, it appears that the aliases chosen for Punch and Judy were intended as an ironic reference to their status as constructs. We have no explanation for why the name Lilith was chosen, other than that it would have been less obvious than Eve, though it does raise another interesting point for fan discussion on religion.
Their actual names, of course, are references to Punch and Judy, characters from a traditional English puppet show dating back to the 16th century in the real world. Whether such a show actually exists in the Girl Genius universe is unknown.