Can I ask a buyer's bank or lender to keep my information confidential too?

Yes, and it's a reasonable request when a buyer's financing means their lender will be reviewing your financial information as part of underwriting. Many institutional lenders already operate under their own internal confidentiality policies, but that isn't the same as a contractual commitment running directly to you, so relying on it alone leaves a gap in your own protection.

The more reliable approach is making sure your confidentiality agreement with the buyer explicitly extends to their financing sources — either by defining "representatives" broadly enough to include lenders involved in the transaction, with the buyer remaining responsible for their compliance, or by asking the lender to countersign a short acknowledgment before receiving your materials. Raise this early, when you first learn financing will be involved, rather than after documents have already been sent to an unnamed lender you haven't addressed in the agreement at all. A Treadstone business lawyer can build lender coverage into the NDA so this doesn't become an afterthought.