The relationship that Lex has with the Kara duplicate is one of the most disturbing things we've seen in the Berlanti shows so far. The similarities between Lex's behavior toward Kara2 bears remarkable similarities to how a pedophile or sexual predator would "groom" a child or young adult. Caring and gentle on one hand, but domineering and controlling on the other leaving the victim both enthralled and submissive. Very creepy.
That's his job.
The Kasnian General paid Lex Luthor to indoctrinate Kara Too.
This is a gentler version of how a cult programs a normal person into selling flowers at the airport, but only because, sex, drugs, starvation, beatings and sleep deprivation will not work on a Kryptonian.