I very recently had an idea. Here it is:

Of course I don`t claim that this is the definite reason for Azura`s pro Lorkhan actions. But lets use it any way.

So the three 'Good Daedra' inspired Veloth with Lorkhanite ideals because they loved Lorkhan. What did they love about him?

Boethia loved his rebellious passion, his ideals, his heart.

Azura, the god queen of vanity[1], loved his beatiful body. That`s why she`s obsessed with moon imagery. It`s also the reason she`s the Twilight(=Dawn) goddess. Only in the untime of the Dawn does Lorkhan inhabit his proper body.

[1] I just made that title up. I like that title.

Mephala is murder and muredous trickery. Of course she would like the mind of the guy who murdered his peers, for their own good, no less!

But Boethia is deceitful, too. And the heart`s motives are obscure, as is Mephala. Maybe it`s Mephala-heart and Boethia-mind. What do you think?

I forgot where I read it, but it said Azura loves Nirn. (I read it on TIL, I just forget where (forums, OT, books))

Yeah, didn't you know that Azura loves to [REDACTED] her [REDACTED] onto Lorkhan's [REDACTED] and [REDACTED] his moon globes with her [REDACTED]? That's also why her realm is called Moonshadow.

Now, someone hurry up and write an in-character RP fanfic. You know you wanna.

In the Khajiit creation myth, Nirni and Azurah have something of a sibling rivalry, which then translates to the rivalry between the Khajiit and Bosmer.

The three 'Good Daedra' is Tribunal doctrine or propaganda. Let's not forget that the Velothi also included Sheogorath, Molag Bal, Mehrunes Dagon and Malacath, though it would probably be fair to include the rest of the Daedric Princes.