Sats can flow bidirectionally among wallets at different levels.
The Lightning Network acts as a bridge connecting different ecash mints.
Suppose a user receives ecash issued by Mint A, but does not trust Mint A. If they have a self-custody Lightning Network wallet, they can immediately melt the ecash sats from Mint A back into Lightning Network sats.
If they do not have a self-custody Lightning Network wallet but trust Mint B, they can convert the ecash from Mint A to ecash sats issued by Mint B with a single click.
Behind this operation, they request Mint B to mint ecash, and Mint B provides them with a Lightning Network recharge invoice. Then, they request Mint A to melt the ecash and instruct Mint A to transfer the Lightning Network sats to the invoice issued by Mint B.