Do I still owe interest if my closing is delayed because of a lawyer or bank error, not my own?

Generally yes, at least in the first instance. Interest for a delayed closing is usually calculated on a per diem basis for each day between the original closing date and the day the deal actually completes, and this obligation typically runs regardless of whose error caused the delay, because it compensates the seller for the extra days of carrying the property rather than punishing the buyer personally.

If the delay was genuinely caused by your lawyer's mistake or your bank's processing error rather than anything you did, you may have a separate path to recover that cost from whoever was actually responsible, such as a professional negligence claim against a lawyer whose error caused the problem. That is a distinct claim from the interest owed to the seller, though, and pursuing it does not relieve you of paying the seller what is owed under the closing arrangements in the meantime. Because the specific interest rate and calculation depend on what your Agreement of Purchase and Sale and any closing arrangement actually say, ask your lawyer to walk you through exactly how the number was reached before assuming it is fixed or non-negotiable.