Would Averna, the Chaos Bloom allow you to get out all of your lands if you cascade and don't have a lower CMC spell in your deck?
No.
Cascade is defined as:

702.84a Cascade is a triggered ability that functions only while the spell with cascade is on the stack. “Cascade” means “When you cast
this spell, exile cards from the top of your library until you exile a
nonland card whose converted mana cost is less than this spell’s
converted mana cost. You may cast that card without paying its mana
cost. Then put all cards exiled this way that weren’t cast on the
bottom of your library in a random order.”

So if you don't have a lower CMC spell in your deck, you will exile your entire library one card at a time.  Once all cards are exiled, you get to put a land card onto the battlefield tapped.  Then you are done.