Making sure I understand this correctly:

I control a Banishing Light that exiled my own Zendikar's Roil. When I cast The Great Aurora, will I get the landfall triggers from any lands I put onto the battlefield with Aurora?

I believe I would. All the rulings on Banishing Light suggest that the permanent returns instantaneously once Light leave, almost as though it's just morphing from one creature into another. Given that, it seems like Roil will be back on the battlefield before getting to Aurora's land action.

Yes. First, the shuffling all happens simultaneously, then Zendikar's Roil is returned to the battlefield under its owner's control, then the card draws happen, then the land part happens, causing Zendikar's Roil's ability to trigger a bunch of times, then The Great Aurora is exiled and finishes resolving. Finally, the triggered abilities from Zendikar's Roil are put on the stack.

Basically, the Roil returning isn't a state-based action, so it doesn't care that a spell is in the middle of resolving. It's a one-shot effect that just occurs immediately after Banishing Light leaves the battlefield.