At the U.S. Supreme Court on Wednesday morning, the only thing Chief Justice John Roberts seemed to want to know was whether Richard Glossip would have been convicted and sent to death row if the jury had known that the star witness against him lied on the stand.

“Do you really think it would make that much difference to the jury?” Roberts asked Seth Waxman, a former U.S. solicitor general who was representing Glossip before the court.

That question was at the heart of nearly two hours of oral arguments in Glossip v. Oklahoma, in which the court is being asked by both Glossip’s attorneys and Oklahoma Attorney General Gentner Drummond to overturn Glossip’s conviction and send the case back to Oklahoma City for a new trial.

Drummond — a conservative Republican who has defended Oklahoma’s death penalty and pushed to carry out seven executions since taking office — has fought to spare Glossip’s life, arguing that the false testimony played a key role in sending Glossip to death row and therefore his conviction cannot stand.

At Glossip’s 2004 trial, the state’s star witness Justin Sneed, who claimed Glossip coerced him into bludgeoning a man to death, testified that while locked up in the county jail he’d been given lithium to treat a cold, but “I never seen no psychiatrist or anything.”

In fact, Sneed had been seen by a psychiatrist who prescribed the powerful mood stabilizer to treat his bipolar disorder. Sneed’s lie, about the reason he was prescribed lithium, and the trial prosecutor’s failure to correct it, violated Glossip’s constitutional rights.

With the state and Glossip’s lawyers in agreement, the Supreme Court appointed an outside lawyer, Christopher Michel — a former law clerk to both Roberts and Justice Brett Kavanaugh when he was a jurist on the U.S. Court of Appeals for the D.C. Circuit — to argue in favor of upholding Glossip’s conviction. Michel rejected the idea that Sneed’s testimony was false, but even if it was, he argued, it was a lie that would not have made any difference to the jury at Glossip’s trial.

“False is false,” Justice Elena Kagan interjected. “The critical question that a jury is asking is, ‘Do I believe this guy and everything he says, and particularly, do I believe him when he points the finger at the accused?’”

Sneed’s lie might’ve made a difference in some other case, Michel said, one where “the witness is presumed to be credible.” But Sneed was not. “In this case, the witness admitted that he beat a man to death with a baseball bat. The witness admitted that he was testifying in exchange for avoiding the death penalty. The jury already had significant credibility questions about Justin Sneed.”

“I have to say, I find that an odd argument, Mr. Michel,” Kagan replied. “It’s like, ‘This witness was so not credible anyway that we don’t have to consider any further lies that he tells’?”

Kagan was not alone in this concern. Kavanaugh told Michel he “was having some trouble” with his argument about Sneed. “The whole........

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