This is how I’m imagine it:

We’ll have many interoperable ecash federations using Lightning to clear bitcoin between each other. 

Federated ecash would be perfect for everyday transactions. Anonymous, very small transaction fees. 

I’m not aware of any reason why this model cannot scale to billions of transactions per day. 

The federations would be geographically distributed with trusted but anonymous federation managers so they’re difficult for governments to attack and suppress.