#soft-lena

I keep trying to find in-canon reasons for that.

Could it be Lena's? Lena went to and graduated from MIT. (For all non-american fans, that's the Massachusetts Institute of Technology, in Cambridge, Massachusetts - east coast, presumably close to Metropolis. The National City University is - as the name says - in National City (not necessarily related to the real life National City), which is canonically in California / west coast.)

Canonically, genius Lena graduated from MIT at the age of 18 (in 2011) and either was already or started working as an advocate at LuthorCorp that same year, when and where she first met Sam. A year later, Lena was fired by Lex, because she didn't share his hatred and obsession for Superman. Around that time she met Jack Spheer and they started working together from a garage, to find a cure for cancer(s) using nanotech. It wasn’t until 2016, when Lex was convicted to 32 consecutive life-sentences and sent to Striker's Island after (kidnapping Lena and) “turning the sun red” to try and kill Superman (resulting in numerous fatalities), that Lena ended things with Jack in Metropolis and moved to National City, taking over LuthorCorp...

While Lena may have taken some online-courses at NCU, to continue learning and expand her knowledge / in other fields, during that time, she was still living in Metropolis. Boston and a vast variety of high-praised universities in an even wider variety of fields are right around the corner. So, somehow I doubt she would have enrolled in at a decent, but not as high-class university across the country. However, there is a slim chance, she did exactly that, if she had been somehow cut off financially after her fall-out with Lex, and NCU was simply the cheaper choice - for some additional credits, she officially didn’t even need(?). So, she maybe got the sweater via mail? Or/and visited NC occasionally before her permanent move for her studies/exams/I-have-no-idea-how-long-distance-universiting-works?

To my best knowledge, we first saw Lena wearing it while staying with the Arias girls. So, could it be Sam's? "Samantha [...] pulled through by herself as a single mother once graduating school from to one job and city to the next to ensure that she and her daughter would have a future together." [arrowverse wiki]

...I don't know about you, but to me that doesn't sound like Sam ever really went to university, but got to where she ended up (COO for L-Corp) for being a hard worker and through experience ...and for having happened to catch Lena's attention.

Sooooooo.... outside of Lena plainly purchasing herself that sweater to show/feel her alliance to National City folks... What's my non-canon / head-canon explanation for Lena wearing that sweater?

Scenario 1:

Game night at Kara's. Kara trips, bumps into Lena and has her spill her red wine over her sweater. Kara: "Oh, my gosh! I'm soooo sorry, Lena! Here, let me grab you something to change into! I will totally pay the cleaning of your probably incredibly expensive-... is that cashmere!? Oh, Rao..!" Lena: "Don't worry. I got it on a discount from Brunello." Lena grabs the offered sweater, goes to the bathroom and changes into it. Lena, smiling to herself: "Yepp, I'm so gonna walk outta here wearing this and never return it..." (Lena returns to Kara googling Brunello Cucinelli sweater prizes; wide-eyed, sweaty and really pale... Poor thing.)

Scenario 2:

Kara learned that Lena's horrible childhood deprived her of watching Disney and Pixar movies. Kara: "I am so gonna make up for that." Lena: "Do I have a word in tha--" Kara: "No." So, Lena shows up at Kara's apartment after work, still wearing her business attire. Kara: "That won't do. Watching movies and chill requires comfy clothes!" Kara goes and fetches Lena her NCU sweater...

3 hours, two movies, 3 pizzas (3 slices for Lena and 2 1/2 pizzas "slowly" consumed by Kara) and a good amount of ice-cream later: Lena: "This was... actually lovely. But it's getting late. I've got to go. Thank you, Kara. I had a wonderful evening." Kara: "I knew it! Nobody can resist cute widdle Wall-E's charm!" Lena: "...he was really sweet, adorable and excitable, but I associated more with EVE." Kara: "Hey, you are still wearing my--" Lena: "Oh, your sweater? I didn't realize. It really is much more comfortable than most anything I own. And it does smell ni--.. Ehem. Hold on, I'll go change." Kara: "Huh, what? Wait! You know, keep it. It suits you. Soft-Lena is a nice look on you." Lena: "Oh, uh, okay... Thank you again. I will see you Thursday at lunch?" Kara: "Count on it!"