Cyborg Superman arrived at the Fortress of Solitude and used Kara’s blood to access Kryptonian technology and memory files.
The blood tricked the computer into believing that Kara was present and requesting information, and so Cyborg Superman’s demand for details about the mysterious “Project Medusa” met with no objections.
The final scene of the episode revealed just why Lillian Luthor needed Kara’s blood.
My first thought was that the blood draw was the way that Supergirl would be creating its own Superboy-esque clone plot, but Cadmus’ plans were much more dastardly.