Lewis was the only person convicted in connection with the leak of CIA agent Valerie Plame's identity. He was never charged with the leak but was found guilty of perjury.
During Thursday's hearing, Walton said he has received "harassing, angry and mean-spirited phone calls and messages."
"Those types of things will have no impact," he said. "I initially threw them away, but then there were more, some that were more hateful. They are being kept."
Libby's lawyers hope to keep him out of prison both for the appeal and because they believe U.S. President George Bush would be more likely to grant him a pardon closer to the end of his term.