Because he and his family defected from the Death Eaters they were pardoned for their crimes after Voldemort's final defeat and did not serve a stint in Azkaban.
In the end his love for his family drove him to abandon Voldemort to search for Draco. His abandonment of Voldemort led to him avoiding another sentence in Azkaban along with his family.
Following his failure to obtain an important prophecy at the end of Order of the Phoenix, Lucius is sent to Azkaban for a while until Voldemort breaks him out, although he doesn't play much of a role in the series going forward.
By walking away, they are making a clear statement to the Order that they are no longer involved with Voldemort. J.K. Rowling indicated on Pottermore and in interviews that the Malfoys do not get imprisoned after the war.
Because he lost the favor of Voldemort who held infinite more power and control over everything including his family and most importantly his dear son who was seemingly sent on a suicide mission due to Lucius' failures.
Voldemort intentionally made six Horcruxes, but when he used Avada Kedavra on Harry, he unintentionally created a seventh Horcrux. Instead of dying, Lily's love for Harry created a counter 'curse' known as Sacrificial Protection and saved Harry.
The main reason is that Lucius failed to retrieve the prophecy from the Ministry of Magic, put that on top of all the other times Lucius failed, and it leads to him losing any clout he once carried within the Death Eaters.
Narcissa's greatest moment, however, was when she chose to betray Voldemort in Harry Potter and the Deathly Hallows. Not knowing whether Draco was alive or dead, Narcissa chose to lie to the Dark Lord rather than risk losing her son.
Draco's refusal to reveal Harry's identity to Bellatrix was not because he liked him. It was because he believed that Harry was the only chance they had at defeating Voldemort. At first, Draco admired and revered Voldemort until he threatened his family's safety.
The plain answer is no.
In the movie, yes, Lucius Malfoy did start to say the incantation for the Killing Curse before he got stopped by Dobby. However, Jason Isaacs, the actor playing him, stated in an interview that he just said the first spell that came into his head, which happened to be Avada Kedavra.
According to Harry Potter: The Wand Collection (your canon mileage may vary) Lucius did intend to kill Harry using Avada Kedavra prior to Dobby stopping the act... Lucius is a known practitioner of the Dark Arts with his wand, including Unforgivable Curses.
The Malfoys are able to avoid serving time in Azkaban, as they provide evidence that helps the Ministry track down the Death Eaters who had fled after the war. It is also probable that, since Narcissa's lie to Voldemort saved Harry's life, the family is pardoned for their crimes.
Draco Malfoy attended Fred Weasley's funeral. He stood in the far back, careful not to be seen, and after he thought everyone had left, he lingered a bit. He'd never let on that he secretly thought the twins were quite funny, and he was truly sorry he'd been part of the reason that Fred died.
Lucius Malfoy craved authority and recognition. Nothing pleased him more than to contribute to a foundation and be elected to its board; nothing made him happier than to walk down the street and have magical folk either kiss up to him or duck their heads and cross the street. Arthur Weasley did neither.
When Lucius turns on Voldemort due to the reveal of his Horcruxes, Narcissa divorces him, taking 75% of Malfoy's wealth with her.
Draco Malfoy's mother Narcissa was cold, cunning and devoted to the Dark Lord. But she was also a mother, which meant she was willing to risk everything to make sure her son was safe. When Harry survived Voldemort's Killing Curse for the second time, Narcissa pretended he was dead so she could get to Draco.
Harry tried to use this spell himself. The first time was against Bellatrix after she had killed Sirius. His attempt was unsuccessful because, as Bellatrix mockingly explained: 'You need to really want to cause pain – to enjoy it – righteous anger won't hurt me for long…'
Harry Potter and the Deathly Hallows
In this book, Rowling reveals that Bellatrix is the guardian of Helga Hufflepuff's cup (though she is unaware that it is a Horcrux), which Voldemort has entrusted the Lestranges to keep in their Gringotts vault.
She asked him because if Draco was still alive, she had something to fight for. She had a reason to lie to Voldemort. If Draco is alive, she needs to get into the school to see him and protect him, and helping Harry feign death was the easiest way to do that. But if Draco was already dead, she wouldn't have bothered.
They decided that they had had enough of Voldemort and his plan. It was a very bold move, because if Voldemort had not perished, they'd have probably been hunted down and punished for their treason.
Narcissa and Lucius both enjoyed being members of the social elite, and loved and spoiled their only child. Unlike Bellatrix, who did not hold love for her husband, Narcissa truly loved Lucius. Narcissa was very upset when he was briefly imprisoned in Azkaban and became defensive when others mentioned his failures.
At the beginning of this book, he measures it against Lucius Malfoy's showing he still has it and it is intact. Dumbledore explains to Harry in book 4 that since both wands contained a tail feather from Fawkes the phoenix, the couldn't face each other as they'd refuse to destroy each other pretty much.
While disguised as Moody, Crouch attacks Draco by turning him into a ferret. Initially, this comes across as a gesture of goodwill as “Moody” says he did it because Draco was going to curse Harry behind his back. This sort of small detail in Goblet of Fire hides the twist that Moody is Crouch in disguise.
Charity Burbage floats helplessly above a dinner table, as if paralysed. She begs Snape to help her. Voldemort point his wand at her, and a green light erupts out of its end. The light hits Charity, and she falls down on to the table dead, her eyes open and her face splattered with droplets of blood.