I wanted to add a checking account to my account because my debit card is lost. Can I do that?

If you are in the USA, no. Here is a list of the payment methods that are valid in your country: Payment methods that you can use with your Apple ID - Apple Support

If your debit card is lost, report it to the bank and get a replacement ASAP. That can be used as a payment method.

You need to -> Sign in to your Apple ID account page and edit / update your Apple ID details.

https://appleid.apple.com                                                     

On the Sidebar click Payment methods -> then tap Payments Methods and tap Manage payment method

Or -> Add a payment method to your Apple ID

Add a payment method to your Apple ID – Apple Support (UK)

• If you want to change your card, you need to add first the new card, then remove the old card.

If you update your payment method or add funds to your Apple ID balance, It would take about 1 to 3 business days in order to process.

If you're still unable to update your payment method, Contact Apple Support.