I went on google and I could see that Lux and ezreal were together .. except that I noticed that on some of these photo garen overproteg ... what I had never seen in the old series of Lol and Valentine's Day Riot. So I wonder is it true that he's overprotective or is just a Fan Art.
Lux and Ezreal never were together in the old lore and in the new one they are canonily not together (see Lux' taunt to Ezreal). There are lot of (great) fanart and fanfiction, but there is usually very little champion interaction in the canon lore.
Garen was never overprotective, considering he shipped his sister off to a military brainwashing camp and then proceeded to mostly ignore her for the rest of his life. In the old Lore, in fact, they barely knew each other as adults.
They're on friendlier terms in the new Lore, although nothing seems to point to Garen having a vested interest in Lux's personal life.
please use this link and scroll down a bit to my comment about ezreal and lux
https://boards.na.leagueoflegends.com/en/c/story-art/75EpeEiF-relationship-in-league
i tried my best to be informative about it.
also if you read garen lore you see that he loves his sister yet he cant get that close to her.so i would say no he is not a overprotective brother.
"Though Garen's sister, Lux, had followed in her brother’s footsteps, coming to serve the crown in Demacia’s capital, their relationship remained distanced. Garen refused to acknowledge the things he’d suspected of her before he left to train with the Vanguard. Though he always loved his sister, some small part of him had a hard time getting close to her. He tried not to think about what his duty would force him to do if his suspicions were ever confirmed."
if garen is overprotective it means he wants lux for himself
