I am doubtful that Lena has figured out Sam is
Reign. She didn't look nearly half as scared as she should be, if she thought the woman who nearly killed Supergirl was standing in front of her. I wonder if she just thinks Sam is exhibiting multiple personality disorder, her very own Sibyl. A problem for sure, but not one that could potentially kill her and her (other) best friend.
We're talking about Lena Luthor here -- a Lena who just decided a week ago to embrace her mother's devious cunning and to use it for good. She doesn't scare easily, and if she were scared, she'd contain it and remain in control of herself and the situation.
Recall that several weeks ago, Lena was present at CatCo when Reign burst into the offices to make her speech to the public, so Lena has seen Reign's face and her eyes and heard her voice. So when she saw Sam's eyes flash red and heard her speak in that imperious tone, she probably put the pieces together. She said "I know what's wrong with you," a statement of certainty, not guesswork.
If she does know Sam is Reign, I hope she tells Team Supergirl. I get annoyed when characters keep secrets from their friends just to create more drama.
I'm not a fan of secrets either, but Lena doesn't really think of Team Supergirl as her friends. Kara and James are her friends, but she doesn't know they're superheroes. She's acquainted with Supergirl and Mon-El, but she doesn't consider herself as close to them. And I'm not sure how aware she is of the DEO; last week, when J'onn recommended getting her out of the DEO before she recovered, suggested that she's not in the loop there. So there's a good chance she will keep the secret to protect Sam.
By the way, when Supergirl and Alex were arguing about whether Julia was a real personality or just a trick of Purity's, I wish Kara had said "You remember Caitlin from the wedding? How she changed to Killer Frost when she got scared? This could be the same thing." Heck, their eyes even change the same way. But the
Supergirl producers seem to be trying to ignore "Crisis on Earth-X."