Lyon v. Pollard was a United States Supreme Court case that dealt with the issue of whether a state court had the authority to issue a writ of mandamus to a federal court. The case involved a dispute between two parties, Lyon and Pollard, over a contract for the sale of a steamboat. Pollard had obtained a judgment in a state court against Lyon, and sought to enforce the judgment by obtaining a writ of mandamus from the state court to the federal court. The Supreme Court held that the state court did not have the authority to issue a writ of mandamus to a federal court, as the federal court was not subject to the jurisdiction of the state court. The Court further held that the state court could not interfere with the proceedings of the federal court, as this would be a violation of the Supremacy Clause of the United States Constitution. The Court concluded that the state court had no authority to issue a writ of mandamus to the federal court, and the judgment of the state court was reversed.

In Lyon v. Pollard, the Supreme Court was asked to decide whether a state court had jurisdiction over an action brought by a non-resident plaintiff against a resident defendant. The majority opinion held that the state court did not have jurisdiction because it lacked personal service of process on the defendant and thus could not exercise its power in this case. Justice Field dissented from this decision, arguing that due process requires only reasonable notice of suit before judgment can be entered against someone who is absent from the forum where suit is filed. He argued that since there was sufficient evidence showing that Pollard had received actual notice of his pending lawsuit through publication in newspapers and other means, he should be bound by any judgment rendered against him even though he never personally appeared or answered in court. Furthermore, Field argued that if states were denied jurisdiction over cases involving out-of-state defendants simply because they failed to serve them with process then many wrongs would go unpunished as those living outside their borders would effectively become immune from civil liability for their actions within another's territory.