In one episode, Konata goads the girls into attending an anime music concert with her. Due to her shortness, though, she ends up not being able to see anything, at which point, Kagami, noticing this, trades seats with her. Konata then appears dazzled with the performance and honestly touched by Kagami's act of kindness. On the way home the other girls comment she is being quiet. Konata dodges the comment then says to herself, "What is this feeling?"
As Konata's sexual orientation is anything but clear, its hard to say if this is really Ho Yay, but, as she seems relatively unaroused by the bodies of her naked friends (though she can be ambiguously gay), its a safe bet Konata was simply reflecting of Kagami's kindness towards her which she later repays during their visit to Kyoto.
You can't tell that just because she doesn't nosebleed into the pool when she's naked with her friends. Do gay menin the Army get instant boners when they shower with their mates?
Kagami from the OVA, "I want to *** with Konata!"
Though it may have happened as a byproduct of the anime adaption, the relationship between Konata and Kagami in Lucky Star seems to extend into Romantic Two-Girl Friendship territory. They see more threads at /u/ (4chan's yuri board) than any other couple, including canon ones.
Or at least so the Fan Fiction writers all believe. Most of it happens in episode 8 I think: first of all Konata refers to her "friendship" with Kagami responding "don't use words like friendship" (which leads me to believe there is some subtext in the original Japanese)- the joke is that Konata just wants Kagami's purchase points- with Kagami thinking to herself "That's what she thinks friendship means". Then while on the bus they are discussing email addresses and Konata annonces her address is "iluvgirlswithglasses", (remember Miyuki?). This by itself disturbs Kagami, but then when Konata goes on to say she wanted "iluvshrinemadiens" but it was too popular, Kagami really freaks out (since she and Tsukasa are actual shrine maidens).
It's really left up to interpretation. Is Konata just an innocent twisted byproduct of her pervert father playing Dating Sims with her, and unaware of the subtext of her comments? (Doubtful). Is Konata aware of the subtext and making the comments (and then playing dumb about it) mainly because she enjoys flustering Kagami and because after all, Konata loves invoking anime tropes, and Les Yay is something that occurs? (Suspicious). Or is Konata actually romantically interested in Kagami. (Plausible) Which ever, I can't help but believe this an invoked trope by the writers, as it is a show all about the crazy antics of okatus it wouldn't be complete without vague Les Yay occurrences for fans to go Squee!, Squick, and debate over.
Konata: The fact that you worked so hard on making this even though you suck at cooking totally turns me on!
Moderately suggested by "official" extras like Kagami's (Emiri Katou's) music CD, in which she sings rather affectionately for someone in a different class, who copies her homework and "gets emotionally moved at anime concerts."
Possibly lampshaded with Hiyorin, a character seemingly obsessed with Ho Yay who can't help shipping her two closest friends with one another and drawing romantic doujinshi based on them.
Maybe it's just me, but does this scene seem vaugely Kagami/Miyuki?