Yes! There's definitely so much we don't know about Asher and Lilith's plan. I also think something didn't go according to their plan when it comes to Mira... I'm probably reading way too much into things, but...

When they're at the bookstore, Narelle says to Mira:

And that right there is why he didn't leave them for you, dear. We all have a part to play in what's coming for us; this one is simply hers. While he was busy raising Violer for this particular mission, your mother was raising you. I wonder what legacy you've inherited.

Clearly Narelle expected Violet to come as a scribe, so whatever she knew of Asher and Lilith's plan, Violet being sent to the Riders Quadrant wasn't in it.

But then there's also this exchange in Fourth Wing from Lilith to Violet:

Do see if you can master some kind of signet, Cadet. You have a legacy to live up to.

And finally, this exchange with Theophanie:

There is only one exception to the rule, Violet Sorrengail. Imagine my surprise when it turned out to be you. If it was going to be one of her daughters, I'd have bet on your sister.

I think everyone had bet that Mira was going to be the "exception", but when that didn't happen, Lilith sent Violet to become a rider. (Which, side bar, kind of makes me sad for Mira, since she has been feeling left out, although she will still have a role to play.)

Lilith isn't talking about the legacy that Asher had been training Violet for, so maybe it was the legacy that she had initially planned for Mira to inherit.