Why didn't Lena know Kara is Supergirl?
My headcanon, completely ignoring the whole Lena and James thing, is that Kara and Lena started dating somewhere during the whole Reign situation, but Kara convinced Lena to keep it between them to avoid everyone judging Lena for being a Luthor. Lena accepted this thinking Kara wanted to avoid being a reporter that was dating a public figure.
After many interrupted dates followed by the news of Supergirl saving the day, Lena is almost sure Kara and Supergirl are the same person. She decides to ignore this and let Kara tell her about her secret identity when she is ready.
But her world is turned upside when she tries to help Sam. She is judged by Supergirl because she is a Luthor, but Kara holds her when she grows frustrated for not being able to help their friend. Lena wants to ignore her previous suspicions, but one day she can't do it anymore, not after fighting with the hero that has the same eyes as the woman that has become her home.
Once Reign was defeated, Lena couldn't wait any longer. While Kara was holding her, she begged Kara to tell her the truth, was she Supergirl? She began crying when she asked if her girlfriend was the one to judge her all those times, she told Kara that she would be with her always, that she wanted all of her and they could write a whole new chapter in the Luthor and Super's story. Kara looked her in the eyes and told her that she wasn't a superhero, she was even joking about Lena having to settle for a simple reporter. Kara held Lena the whole night, whispering sweet nothings and making Lena feel completely loved for the first time. Lena felt that she could finally trust someone with her whole being.
Lena could still see the similarities after that night, but she believed in Kara. She finally had a family that accepted her, she was having a better relationship with Supergirl and she was sure Kara was the love of her life. She just wished their friends knew about them, after all she had been dating Kara for almost two years by that point, but she was sure they would tell them in a short time.
Lena kept carrying her biological mother's ring in her pocket, waiting for the perfect moment. That's when problems arised, Lex was free, but Lena kept carrying the ring. She decided that the moment Lex was defeated, she would get down on one knee, come rain or shine. But her plans were just plans, Lex told Lena about Kara's betrayal while he was agonizing. The rest is history.