As Oklahoma prepares to carry out seven executions over a five-month stretch, the U.S. Supreme Court will soon hear oral arguments in a case that could expand civil rights for the condemned.

Convicted of murdering a convenience store worker and sentenced to death in 2008, Texas prisoner John Henry Ramirez was scheduled to be executed on Sept. 8. In the weeks leading up to the execution, Ramirez requested that his pastor be allowed to lay hands on him during the administration of lethal injection drugs.

Texas prison officials rejected Ramirez's petition, citing safety concerns. This prompt...