AU scenarios in all honor, as far as actual canon analysis goes “Yotsuba!Light loves L” is probably one of the most bizarre ones of the pervasive takes out there.
Light has no reason to like L during that timeframe. For the longest time, has no reason to even believe L is actually smart.
From his perspective
L arrested him entirely wrongfully.
L is now refusing to make amends for this arrest that harshly damaged his relationship with his family and academic career.
In fact, L is planning to keep him captive indefinitely because he’s “just not motivated”.
L then spends two months doing absolutely nothing while Light is trying to investigate to get his freedom back despite L’s complete non-cooperation.
Towards the end of the arc Light finally comes around to the idea that he might have been Kira and lost his memories, but for the vast majority of those months he thinks of himself as innocent and watches L refuse to admit so because he’s sulking about having been wrong. That’s not… likeable.
That’s especially not likeable when your whole life depends on that guy’s judgment and he’s told you in no uncertain terms that he doesn’t care to release you or change his mind on you.
And thus…
It’s worth pointing out here that there is no other situation in which Light ever physically lashes out. That kind of behavior is entirely uncharacteristic. For his control to slip enough to try and break L’s nose… twice? Yotsuba!Light is desperate and a lot of that is due to L.
The Yotsuba arc is the arc in the manga during which Light smiles the least. Volume 6 is the only volume in all of Death Note during which Light does not smile even once. He is miserable.
All of Light’s attitude in the Yotsuba arc is informed by him being on best behaviour because he’s literally a prisoner and his freedom depends on convincing L that he is a good innocent person.
I do think that at the very end of the arc L and Light do begin seeing somewhat eye to eye but it is a hard process and 90% of those months are spent in mutual disdain of each other.
(If you have like an hour, I recommend reading the analysis Hellscape to get a picture of Light during the Yotsuba Arc.)
