I honestly don't understand why so many people hate this ship just because it looks so stereotypical. When you look at the finer details of the ship, it isn't really THAT stereotypical. Yes the shipping is really damn cute (LuxReal is my OTP, fite me), but there are numerous reasons I could name for why this shipping is reasonable.
(Fair Warning: Wall of text and that I got this idea of the OP's comments in this post. I just really wanted my opinion on the shipping and that I want to expand it.)
First of all, if you read the lore, you know Lux was drafted into the military ever since she was a teenager, and you know what happens to people that go into the military. Then, she grew to love her country out of peer pressure (from countrymen and most especially, her family) because she's a noblewoman. From her laugh itself, most, but not all, may say she's a "destroyed" girl that actually wants to be free from being caged by Demacia. Also from her League Judgement, she joined the Institute of War because it's the only thing left that could allow her to escape her harsh reality of being imprisoned by politics. Lux has a complex relationship between herself, to Demacia and to her family that she's willing to not talk about it to anyone but keep it to herself because for all we know, she's very selfless in that she prioritizes her country's ideals and needs over her own and let's be honest, if you were to put yourself in her shoes, it hurts a lot on the inside. Let's also say that she's really depressed on the inside because of what had happened to her in the past.
Ezreal, on the other hand, lived his life as a freelance person. He has no parents (read his updated lore in the wiki to understand this), he has all the freedom in the world, he explores the world and that he has both wits, smarts and a little luck and that often times, he loves to work alone. Sounds like your typical Shounen anime protagonist amirite? However, with the little contact he had to magic (his gauntlet), it made him famous because it's magic, and that possibly, the summoners knew of his potential so they put him in the League of Legends which in turn, really made him a superstar in everyone's eyes. Ezreal actually hated this, but grew to adapt to it because this became part of his life when he found his gauntlet and that he loved adventure. And let's just say he's fairly arrogant, a bit selfish (because he often does his job), a little bit ignorant and confident because, character reasons and Rito Games.
So now for the readers who read this, you know that their personalities and social standings are very opposite, but let me explain further.
Now imagine, if (a really big if) both Lux and Ezreal crossed paths. Yeah sure, they'd make some small talk about the current events. But this is where things get spicy. They decide to get real and talk about their own lives and when Lux decides to open her life to Ezreal, he now begins to understand that everyone doesn't have the same liberty of living life freely as he did. Now as Ezreal begins to tell about his adventures, this is where Lux views Ezreal as a visual representation of the freedom that she longed, but let's just say as well she also realizes that freedom is also a privilege and like everything, it can be taken away by anybody and that's why Ezreal's often a loner, no parents, no guardians (except Professor Lyte and his uncle that really don't care that much about him either way) and that he lived through life through wits, smarts and a little physical capability.
So now, both blondies understand each other's lives and their pros and cons. As for Lux's case, she wants to be free of her duties, but not completely abandon them and that Ezreal actually wants to help her at least have that small bit of freedom. In exchange though, Lux helps Ezreal augment his magical capabilities and to be his light (pun intended) in his adventures and that Ez would like some company in his trips. Despite their opposing jobs with Ezreal being a nomadic explorer and Lux being a noblewoman, they still find time to spend time with each other, whether it be inside or outside the Institute of War. Well overtime, they start to fall in love with each other and the rest is up to you.
Even though Lux X Ezreal is my OTP (dammit, this shipping is so cute I can't resist saving fanart of it), I don't see this as a long-lasting relationship but rather, as a "teenage dating/comfort" kind of relationship because of the circumstances of their social standing. But then again, their love story would make a great romanace/drama fanfic or a shounen/shoujo & romance anime/manga. I dunno, Riot really loves to Ship Tease the fandom really loves to ship characters because why the %$@#! not?
As a side note, is it bad that I say that I have a stash of Lux X Ezreal fanart in my desktop? I wonder if people would find it a bit creepy. But there you go, my wall of text that may or may not be reasonable to you.
Edt: I fully agree with the expression that this shipping is not one-sided because people who think this shipping is one-sided are biased towards one of the characters but mostly being biased on Ezreal because of his personality. People need to stop viewing Ezreal as too rash and stereotypical of a character.
Extra Edit: But seriously, if League had a Shounen/Shoujo, Romance and Adventure anime, I'd ship Lux X Ezreal so hard and the theme song would be a toss up between the following:
Endless Starlight
Crossing Fields - SAO Soundtrack
Varien - Valkyrie (Monstercat Release)
(Really sorry if my tastes for this shipping are a bit too cliche.)