There is no explanation of why she joined the league of legends. All it says is that she vowed never to return to the sea until she had completed the Tidecallers quest.

If I have somehow missed something please point it out but If not I really think the lore should be updated and give an explanation to why she joined the league.

Ive heard that IronStylus said Shes connected to Diana and Leona somehow
probably gnna be explained later

Taric is probably the reason why Nami joined the league. Re-read her lore, look for what Nami is looking for... then look at Taric and his gorgeous gems.

Well, my guess is that she joined the League to use the influence from it to help her with her quest. The more recent stuff lacks any official reason for them joining, sadly.

I would go with publicity as the explanation. She needs the human that she's trying to find for her quest to notice her, so what better way to get noticed than joining in on what is perhaps the biggest public spectacle in the country.

But srsly if she want to complete her quest, the League is the last place for her to be.

Why? Think about it:

One: Look at the positioning of the Institute of War. It is RIGHT IN THE MIDDLE of EVERYTHING! What better place to start looking than the center?

Two: Remember how influential, powerful, and knowing the Summoners are, if they have any idea of where the Moonstone she is looking for might be, or have any idea of where to start looking, THEY are the right people to befriend.

Three: And this has been pointed out by EVERYONE; but the Leageu is incredibly popular and showboating (let's be honest, it is) if anyone knows about it all across Valoran, her, her people, or the item she seeks, and they see her talking about it while watching a match, they will know where to find her.

Of course; with her in the League and fighting for it now, there is a possibility that she may NEVER get what she seeks because the Summoners don't want to lose a champion. If she gets the Moonstone she'll take it back home and never return, and the League would be down one fighter in their grand show. There's an element of political courrption to this theory, but it IS a possibility.

Why is she wasting her people's time fighting instead of searching. Or better yet, if she can live on land, why don't her people leave that hazardous deep sea.

She IS searching. You never try looking for something that you have NO idea what it looks like or any idea where it might be in a place that you have no idea even existed until a little while ago? Go to Tibet and look for a Samoplange in one of the caves; not so easy, is it?

Also: YOU can live wherever, why not live in Spain, Japan, or England! But that isn't the best example:

Keep in mind; while Nami and her people can apparently breathe air (typical for a mermaid) they cannot walk on land. The only reason Nami is there is because she can control water to carry her across (heck, she may actually be using the same magic to breathe!) the land. But surely they could move to some lake or something?

You ever see a lake large enough to not only house but to act as a toilet and food supply for an entire civilization? As for the more open ocean; again, not enough resources.

Sorry if I sound a little rude but you seem to be overlooking basic concepts, and it irritates me a little. I do appologize if my words irritated you in any way, however.

if u put it that way,why xerath would join lol?to gain power and free his self of his chains,while he knows that the "summoners" will never let him get that power?
why zed joined lol?to kill shen,while shen is the one who should seek revenge on zed?
anivia?joining lol to bring other ice elementals?pls
and the most annoying of all,champs who dont even actually have a lore,like karthus,shaco and eve