What is the effect on a lower court ruling when an appeal is pending before the US Supreme Court?

There is usually a "stay" on the lower court order, preventing any action from being taken until the US Supreme Court rules.

If the case has simply been petitioned to the Supreme Court for a writ of certiorari, and has not (yet) been accepted for review, the lower court must agree to the stay, or the US Supreme Court must override their refusal and grant an emergency order.