I'd like to ask if there is a difference between these verbs in terms of meaning, formality etc. in the following sense. Can you change the words between the sentences so as to see if they are interchangeable, please.
To lie with
To be somebody’s duty or responsibility.(formal)
It lies with you to accept or reject the proposals.
To rest with
If it rests with somebody to do something, it is their responsibility to do it. (formal)
It rests with management to justify their actions.