The customer visits bank and is provided a "bank account" which is a managed address on the bitcoin blockchain. The customer can still have personal addresses, but this address will be secured and guaranteed by the bank and have attached banking services.
thats your "theory"
the actual reality is blockstream will be the LN hub that holds peoples funds in a multisig of them having 50% permission of funds, so they can 'manage' and set penalties.
banks already are investing in blockstream and blockstream have to develop LN commercial hub service to repay bankers investment through the LN fee's. but banks wont actually integrate bitcoin as a bank service direct..
banks wont handle bitcoin. they are going to have their own fiat 2.0 called hyperledger sidechains.
also why oh why are people actually advocating to turn bitcoin into a permissioned service that is tethered to banks. indirectly via investment. deluded to want banks to hoard peoples funds directly... seriously!! wake up