Lena knew Kara was Supergirl. She had known from the very first day they met. When Supergirl came in to save her from what was almost a helicopter crash, Lena had seen a strange scar next to Supergirl's left eyebrow. She'd seen that exact same scar earlier that day, only then it had been upon the forehead of a silly young girl calling herself "Kara Danvers". That was Lena's first clue that Kara was Supergirl. The scar on Kara's forehead was way too similar to the scar on Supergirl's head for it to be sheer coincidence alone.
But that wasn't the only trait that Supergirl and Kara shared! As Lena came to know, they shared many other facial features/structures in common and there were at least a million little traits and quirks that the two also both possessed. Kara and Supergirl looked and sounded the same, they also talked, walked, thought and behaved much the same and they had the same beliefs and temperaments. They could've been sisters! But Lena knew better. It was more than simple sisterhood that bound them. They were one in the same.
From that day forward, the evidence around Lena's theory of Kara being Supergirl only increased. There was the fact that they were never ever seen in the same place at the same time. There was the fact that whenever one was present, the other would vanish. There was Kara's "special connection" to Supergirl. The list went on!
Finally, though, Lena stopped counting how many clues she had found. Now, she was counting how many days it took for Kara to just come clean and admit to Lena's face that she was Supergirl. It was painfully obvious, so why was Kara so bent on keeping up the lie? In all the years Lena had known Kara, the girl was always adamant about hiding the truth from her. Lena wanted to know why, and how long, Kara was going to do this for. But as much as Lena wanted to know, and as much as it hurt her to think that Kara didn't trust her enough to confess, Lena already knew she'd never call Kara out on her lies. Nor would Lena ever force Kara to "out" herself. This was for two reasons.
The first was basic respect. Though Lena hated being lied to, especially by a friend and especially in such a pathetic manner, she still refused to out Kara. This was Kara's life and Kara's secret. Lena had no right to try and dig it out from under her. Kara would tell her when she was ready, and even if that day never came, it still wouldn't be right or honest or fair of Lena to try and force a confession out of her. So for that reason, Lena refused to ever call Kara out directly. She dropped hints frequently, always offering to listen if Kara ever had anything important to tell her, but she never pushed the girl into a confession. Lena had her own secrets, so what right did she have to demand the secrets of others? She liked her privacy just as much as anyone did, so it wouldn't be fair of her to ask Kara to sacrifice her privacy when she, herself, had plenty of things she'd never told anyone else, including Kara. So instead of demanding, Lena waited patiently. If Kara wanted to keep it a secret, Lena had to respect that.
The second reason was a bit more selfish. The other reason Lena didn't call Kara out was because she wanted Kara to tell Lena herself. She wanted Kara to come to her, not the other way around. Lena wanted to believe that Kara loved and trusted her enough to tell her the secret on her own. How could that happen if Lena were to try and pry it out of her prematurely? No, if Lena wanted to know how Kara really felt about her, Lena was going to have to let this secret, however flimsy, stand, and see where it would go. Would Kara prove that she did trust Lena and tell her? Or would Kara forever remain distant and keep this "secret" from her? If Lena wanted for Kara to prove that she trusted her, Lena was going to have to let Kara come to her, frustrating as such an idea was.
Mostly, it frightened and hurt Lena to think that Kara might never trust her enough to tell the truth, but Lena had long-since resigned herself to that idea. She had accepted the fact that, unpleasant as the idea was, it was Kara's right to be this way. Kara had a right to keep her secrets. Kara had a right to not trust Lena. Besides, Lena really did want Kara to tell her the truth of her own free will. It wouldn't make Lena feel good if Kara were to tell her the truth because it was forced out of her. What would really make Lena feel loved and respected, selfish as it was to say, would be if Kara told her because Kara chose to, because Kara decided Lena was worthy of knowing and keeping the secret. In this case, it wasn't the secret that mattered, so much as all the trust that it represented. Lena wanted the secret because she wanted Kara's trust, not because she wanted the secret itself.
So for now, Lena would only wait. She would watch and insinuate, but she would not push or call out. Instead, she would wait. She would wait for the day Kara felt ready to tell the truth. She would way for the day when Kara decided to prove that she trusted Lena enough to tell. She would wait for the day when Kara confessed of her own free will and choice, not through coercion or demands. She would wait for the day she received the secret and didn't have to take it. She would wait until the day Kara came to things on her own times and terms.
Then, upon that day, Lena would finally know that Kara really trusted her, and that she deserved to be told the truth, and she wouldn't be upset at all, no matter how long the wait ended up being. She would wait for the day the truth was freely given to her, even if that day never came. Why? Because when it was Kara, she would wait forever.
AN: Just a short drabble on why Lena hasn't "realized" that Kara is SG yet. IMO, she knows (figured out on Day One), but she's waiting for Kara to tell her.