On the stand Monday, Malvo's father recounted early days with his child, innocent times watching planes and riding bikes, reports CBS News Correspondent Scott Rapoport.
Jurors met for three hours without reaching a decision. They are to resume deliberations Tuesday.
Malvo, 18, was found guilty last week of murder in the killing of FBI analyst Linda Franklin, who was cut down by a shot to the head. It was one of 10 slayings that gripped the Washington area with fear during three weeks of shooting attacks in October 2002. Malvo was 17 at the time.
Last month, a jury in Virginia Beach convicted Muhammad, 42, of murder for another of the sniper killings and recommended the death penalty.
During Malvo's trial, his lawyers mounted an insanity defense, claiming indoctrination by Muhammad left him incapable of telling right from wrong. The jury rejected that defense, but it formed the basis of the attempt by Malvo's lawyers to save his life in the penalty phase of the case.
"There is no such thing as a self-made man," defense attorney Craig Cooley said in asking the jury to sentence Jamaican-born Malvo to life in prison without parole. "Lee was uniquely susceptible to becoming attached to a father figure in the charismatic personage of John Muhammad."
He added: "Every person, certainly every child, has good within him. Every person is redeemable."
Cooley said Malvo's absent father, plus a mother who beat him and moved him constantly, left him susceptible to Muhammad.
"Children are not born evil. When they commit evil acts, you can almost always trace the acts to the evil that has been performed against them," he said.
Prosecutor Robert F. Horan Jr. argued that Muhammad's influence makes Malvo no less culpable. Projecting onto a large screen photos of victims of the three-week spree, the prosecutor said that Malvo "chose to kill without compunction, without compassion."
Referring to the shooting of Franklin, Horan pointed to Malvo and said: "He did it, not John Muhammad. He's the sniper. He's the shooter."
Horan told the jury that the death penalty was appropriate because the random slayings were "outrageously vile," one of the requirements a jury must find to recommend the death penalty in Virginia.
"They started out by killing innocent people before they even told the government" they wanted $10 million, Horan said. "If there is such a thing as vileness, that is vileness."
Malvo's estranged father testified for the defense during the sentencing phase that his son had wanted to be a pilot from the age of 3. Leslie Malvo said he bought Lee a jacket emblazoned with the word "pilot."
He said he and Lee would sit at the back of their house in Jamaica and watch planes land. "Lee loved it very much," the father said.