So, it seems to be floating around that Garen has a massive overprotection urge towards Lux. I've seen it in a few of the fan-made Mangas, some other stories, but I haven't really seen anything in the official lore about it.

So, why is Garen seen as such an overbearing/overprotective/siscon towards Lux?
I'm mostly just curious about the origins of this. If there is a lore-based reason, I'd like to know that as well.

brotherly sisterly thing you woundlnt get it unless you have one

I don't see them being close at all (and it's reflected in my story).

There's nothing in the lore to suggest they have a close relationship. If anything, Lux's judgement shows that Garen is rather indifferent (if that is actually him and not an illusion created by a summoner), and Lux seems to have no inclination that way either. She doesn't even greet him upon seeing him for the first time in years.

In my personal opinion, Lux might actually resent him for disappearing and not contacting her even after she 'joined' the military. Wouldn't you be a little upset if that happened?
On another note, Lux is rather selfish, and is focused on her own goals rather than Demacia's, unlike her brother. Garen lives for Demacia, and will die for Demacia. As much as Lux loves her home, she hasn't decided what's really important to her yet.

So please don't fall for the whole 'more than siblings' thing. It has little to no base. :/

Lux is so moe. Garen's overprotectiveness is a manifestation of the author's feelings.

Just my theory.

Frankly, I'd say that's a sign of how good a person she is. Consider how she's been treated by her country of birth; she's been torn from her family at a young age, forced to do something she didn't want to, been indoctrinated and brainwashed to better serve the state. It's a wonder she does't outright hate her city state. A little selfishness is hardly anything considering what she's been through, and I'd also question whether she truly love Demacia, or simply serve because that's all she's ever known.

Imouto Complex.

It is a silly trope that some people apparently like to use just because.

Because what we've got is vague and people like to fill in the blanks.

But I like to think that the characters are human beings, and not mindless drones, and assume that Garen wants to make up for the times he wasn't there for her.

I agree with Ceru. That's exactly what I thought when I finished Lux's Judgment.

Garen is her brother