Our nonprofit received a 1099 for consulting services to another agency. They will be paying the non profit a lump sum. Our executive director who is on our payroll, was the actual one doing the consulting so do we send through payroll? Or 1099?

This depends. Theoretically, you could actually do either option. However, it might be more convenient for the director to have it issued through payroll, so that the appropriate taxes can be withheld. It would also eliminate the need for you to issue two year-end forms for him (a 1099 and W-2). I would consult a tax professional to make sure.