[Vexx]

There's also some assumption here that Konata isn't "ready for play" that is incorrect.
It is being based off of Kagami's hyperbolic speculation in an embarrassed moment -- since Konata is 17, Kagami is just blowing mental smoke...

And the synchronization *trend* is noted for all races.. not just asian and not just family members but anyone in long term close proximity. Though it is a statistical *trend*, not a given.

As far as the seriousness in this episode:
Lucky*Star has some very serious moments amongst the comedy -- it makes the comedy more dear because you know there's some poignancy underneath:
1) Kagami wanting to fit in and not making friends easily
2) Konata not ever quite understanding her ADD nature of impulsiveness and inability to track on schoolwork while hyperfocusing on videogames.
3) Nanako really not having anyone despite being a really wonderful and playful person.
4) Miyuki's long list of little fails underneath her "miss perfect" persona.
5) Tsukasa's fragile self-esteem and over-dependence on her sister

6) etc etc etc

These foibles make the funny more human and more directly hits the target.