riot is not doing a great job on their lores since lulu

Can someone tell me why she is in the League?

I mean, if she is on a clock and all...

Which is why she joins willingly so that the Summoners see no reason to imprison her. The League would be more likely to imprison her and limit her powers if she was a rogue entity threatening the world. By joining the League, however, she can unlock her potential by facing the strongest foes, until she eventually gains enough power that she can destroy/conquer Ionia, and possibly even the League itself. That's how I see it anyways.

Also, I don't really see her getting much practice sitting alone in a floating fortress.

Best place to find someone with a Moonstone, considering people from everywhere, even the Void and Shadow Isles, come there. It's the quickest way if you think about it.

Also, the Kalamanda incident showed that the League doesn't really give a Twitch's tail about time.

Don't forget that League events are "televised". If there's someone wandering around with a moonstone this increases the chances of them knowing someone wants to trade for it.

So she turned herself into prison so the cops didn't come and arrest her? Probably not the choice Syndra would make, seeing as she's power-hungry and defiant. Besides, the end result is the same. >.>

The fact that she's in the League means summoners have power over her. If she isn't in captivity now, why would the summoners simply let her become stronger and evolve into a threat not even they could handle? You'd think the most intelligent people in Runeterra would think about these things ahead of time.

And about the flying fortress... Yeah, how many people in the world can do that? How much magic power would that require? And how much attention would that garner from the organisation that's trying to limit magic use in order to save the world?

I can't outright say this is exactly what happened, but it's the only way her lore makes sense, as it is now.

I'm going to go ahead and assume that she found the Moonstone before she joined the League. It makes more sense to me that she had some manner of exciting adventure to recover it, and when all of that was over she felt that it was in her people's best interests to have a representative on the surface.

I would further surmise that this has something to do with the Solari/Lunari conspiracy. As other people have mentioned, the only culture that has anything to do with the Moon was wiped out by the Solari. They then erased nearly all evidence of their existence until Diana discovered it.

Regrettably, Diana doesn't know much if anything about the Lunari other then that she has a set of armor and a sword. I would imagine that once they meet up, she and Nami would go on some sort of journey to both rediscover the past and find the resting place of the moonstone. This would lead to them uncovering and potentially exposing the Solari for their crimes. While the loss of the Lunari culture might have been forgotten by everyone, their actions nearly led to the extinction of Nami's people, which would be a fairly heinous crime.

So, after exposing the conspiracy for what it was,Nami then chose to remain on the surface and join the League. It allows her to better serve her people's interests, and it helps her keep on eye on her new found friend. Cue hot, intense, AO-rated fish-on-moon action every night. I mean... um... keeping an eye on that pesky Leona character.

That is exactly the point, negotiate on your terms rather than on the enemy's terms where they will most certainly treat her like Nocturne and Brand, prisoners within the Nexus.

And besides, Noxian summoners will take a liking to her thirst for power and invite her to join Noxus' ranks. Seeing how an Ionian such as her is so willing to embrace power at all costs.

I don't know if you saw my last post which expanded on this. The League is not stupid. They would not knowingly allow themselves to be used that way, especially by someone so violent and unpredictable. And judging by Syndra's very apparent lack of experience and forethought, she would not be able to fool them. Heck, she probably didn't even know the League existed until she started creating mayhem in Ionia.
She's really another case of Xerath. She needs to be contained, or she's going to cause problems - not just to Ionia, but to the world at large.

Also, Noxians are a rather xenophobic bunch. They wouldn't even consider siding with an Ionian after the history between them.

I like this lore much more than some of the recent stories, it feels a lot deeper and complex than some of the stuff that we have been seeing. The only negative thing is the time frame but i like SufferNot's idea, that makes a lot of sense.