Mr Justice Sweeney warned the panel of eight women and four men not to let emotion sway their decision.
He was summing up in the case of Michael Adebowale, 22, and Michael Adebolajo, 29, who are accused of running the soldier down with a car and then hacking him to death with a meat cleaver and knives near Woolwich Barracks in south-east London on May 22.
Both men are also accused of attempting to murder a police officer in the aftermath of the alleged killing. They deny the charges.
The judge told the jurors: "You apply the law as I direct you it is to the facts as you find them to be, and by that we will between us ensure that you return true verdicts according to the evidence in this case.
"Guarding against speculation or emotion entering into your deliberations is particularly important in cases of this type. What's required of you is a cool, calm, careful and dispassionate consideration of the evidence."
He said that in relation to the murder count, the jury must consider three key factors.
The first is whether or not Lee Rigby was killed in the course of war. The second is whether he was unlawfully killed, and the third is whether the defendants were involved in a joint enterprise to kill him or cause him really serious harm.
The court heard that any suggestion that Mr Adebolajo had been engaged in a war of rebellion against the state was not a defence in law.
Addressing the question of intent, Mr Justice Sweeney said there was no psychiatric evidence that either defendant was incapable of forming an intent."
The court earlier heard that Mr Adebowale, who chose not to offer evidence, shares his co-defendant's belief that he is a soldier of Allah. The trial at the Old Bailey continues.