The ruling Monday from the 5th U.S. Circuit Court of Appeals means 44-year-old Ramiro Hernandez-Llanas is set for execution Wednesday.
Attorneys for Hernandez-Llanas and another inmate, Tommy Lynn Sells, had filed a lawsuit saying they needed the drug supplier's name in order to verify the drug's potency and protect the inmates.
The state argued it was protecting the company from threats of violence.
A lower court initially sided with the inmates. But the 5th Circuit reversed that ruling last week for Sells, who was later executed, then Hernandez-Llanas on Monday.
Hernandez-Llanas was convicted of killing a rancher in 1997.
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