Superlane... Lucy is stationed wherever the show shipped her off to and Kara flies out every once so often to see her, go one a date or whatever. They both have a few stressful week and Kara hasn't had the chance to make the trip and she gets home from work one day and Lucy is waiting for her outside her apartment door like, "Since you haven't had the chance to fly to see me, I thought I'd fly to see you," or something less lame than that but in the same spirit of things.
They’re not /dating/ dating, obviously, because Lucy is in another city and Kara has gone from one relationship to another and she really just needs a break and dating her ex’s ex just seems like a bad idea so no, they are not dating dating. But they are dating, kind of, if you consider daily phone calls and Kara spontaneously flying cross country just so they can eat a meal together “dating”, and sure, maybe two weeks before, when they were sitting on the bed of Lucy’s long stay hotel, Kara may have kissed Lucy a little bit. Just a little bit! Barely a smooch; a mouth graze at most. It doesn’t mean they’re anything.
So. They are not in a relationship, and there is no reason for Kara to be moping around her apartment just because her superpower blowout has ruined her plans to spend the day at the Metropolis farmer’s market with Lucy. It also doesn’t matter that Lucy hasn’t responded to her last seven texts, either, because Kara is not her girlfriend so why should it matter? Also powerless Kara totally has allergies, probably, and that’s why she’s been crying and sniffling all day. No other reason.
And because Kara is clearly not in a relationship with Lucy Lane, she’s completely surprised when, after hearing someone bang on her door, she opens the door to find her standing there looking exhausted and balancing a huge box of donuts in her arms.
“I’m sorry I haven’t texted you back, I had to turn my phone off on the plane.”
And Kara’s allergies must be acting up because she’s really crying now as she gathers the other woman in her arms.
“You came all this way for me?” Kara asks, and Lucy looks at her like that’s the silliest question she’s ever heard.
“Of course I did, you goober. I’m your girlfriend, it’s my job.”
And who was Kara trying to fool? She is definitely /dating/ dating Lucy Lane, and she wouldn’t have it any other way.