That all happens in Lightning Network too, it's just called different things. You need to create a channel (create an account, create a token) locking up a certain amount of money (topping it up), and obviously you need to store the credentials for the channel (store the token), and renew it (renew the token) or close it (refund unused credits) every week - that means opening the app at least once a week or you lose your money - otherwise your partner gets all the locked-up money.