No.
If your Amazon credit card has been reported lost, generally the bank will stop using the credit card, so there will generally be no monthly rent deductions. However, if you were using the credit card before Automatic deduction has been authorized during the process, and the deduction may be successful before the loss is reported.
The Amazon Credit Card is a credit card issued by Amazon and partner banks. It is designed to provide users with benefits such as discounts when spending on the Amazon website or Amazon physical stores, as well as benefits such as cash rebates or points.