Lapeyre v. United States was a Supreme Court case that addressed the issue of whether a federal court had the authority to issue a writ of habeas corpus to a state court. The case arose when a Louisiana state court convicted a man named Lapeyre of murder and sentenced him to death. Lapeyre then filed a petition for a writ of habeas corpus in a federal court, arguing that his conviction was unconstitutional. The federal court granted the writ, and the United States appealed the decision to the Supreme Court. The Supreme Court held that the federal court did not have the authority to issue the writ of habeas corpus. The Court reasoned that the writ of habeas corpus was a state prerogative, and that the federal court had no authority to interfere with the state court's decision. The Court also noted that the writ of habeas corpus was not a remedy for constitutional violations, but rather a means of determining whether a person was lawfully detained. The Court's decision in Lapeyre v. United States established that federal courts do not have the authority to issue writs of habeas corpus to state courts. This decision has been cited in numerous subsequent cases, and remains an important precedent in the area of federal-state relations.

In the case of Lapeyre v. United States, the Supreme Court was asked to decide whether a federal court had jurisdiction over a dispute between two citizens of Louisiana concerning land located in that state. The majority opinion held that it did not have such jurisdiction and dismissed the suit. In his dissenting opinion, Justice Field argued that Congress had given federal courts exclusive original jurisdiction over all cases arising under any law providing for internal improvements or granting public lands within any state or territory; thus, he believed this case should be heard by a federal court since it involved land granted by Congress for an internal improvement project in Louisiana. He further noted that if this were not so, then there would be no way to enforce laws passed by Congress regarding these matters as they could only be enforced through suits brought before a federal court with proper jurisdiction.