Is a lease a written agreement between a bank and a borrower?

No, a lease is not typically a written agreement between a bank and a borrower. Instead, a lease is a contract between a lessor (the owner of the asset) and a lessee (the user of the asset) that allows the lessee to use the asset for a specified period in exchange for payment. While banks may be involved in financing leases, the lease itself governs the terms between the asset owner and the user, not between a bank and a borrower.