Lucius Malfoy grew up in a time of chaos, anger, and hatred. Purebloods and Muggle-borns had been at war with each other long before Lucius was born; but tensions only increased with Voldemort's rise to power, and Voldemort was one of the main parts of Lucius's childhood.
With Voldemort, the Purebloods believed that their time had finally come to establish their superiority and to rid their world of the "inferior." The Muggle-borns, on the other hand, believed that Voldemort proved with absolute certainty that Purebloods were evil and that they were the ones that really needed to be eliminated.
Even though most would say differently, the war between Purebloods and Muggle-borns was not a simple matter of evil Purebloods against good Muggle-borns. It was just as common for a Muggle-born to curse a Pureblood as it was for a Pureblood to curse a Mudblood.
Of course, the attacks on Purebloods did not receive as much news attention because Muggle-borns just made better victims. Besides, it was hard to feel sorry for Purebloods when so many of them were wealthy and privileged. At least that was how Muggle-borns saw it. Purebloods, of course, saw it a lot differently, even though they would never consider themselves victims. No, Purebloods were warriors and survivors.
Despite all these tensions, however, life for the most part seemed normal. At least during the day for the most part. Daytime, of course, did not mean instant safety; but if you were going to go out, it was best to do so during the day. Pureblood or Muggle-born, you went out at night at your own risk.
Of course, there were many wizards and witches from both sides that boldly made their presence known as soon as night fell. Depending on who you were talking to, night was best time to take down a filthy Muggle-born or a vile Pureblood. It was harder to see when it was dark, and less people were out. Regardless of blood status, you were more vulnerable at night.
Abraxas Malfoy was one of those Purebloods that boldly conducted much of his business at night, and his son Lucius often accompanied him. Abraxas, wanting to maintain the appearance of a caring father, insisted that he only took Lucius with him because he didn't want to leave his young son alone at the manor with only house-elves to look after him. Lucius's mother had died in childbirth, leaving Abraxas as a single parent.
In reality, though, Abraxas wanted his son to see with his own eyes why Muggle-borns needed to be eliminated. Some lessons were best learned through personal experience.
Muggle-borns living in poverty were always ready to attack a wealthy Pureblood that looked vulnerable. According to the Muggle-borns, they had to do this because the wealthy Purebloods had oppressed them so heavily and had denied them opportunities to truly succeed in life. According to Purebloods, on the other hand, Muggle-borns were poor because they were lazy and unmotivated. They were rather give in to their petty jealousy and rob a wealthy Pureblood than actually do some real work in order to make their lives better.
Regardless of who was right and who was wrong, both Muggle-borns and Purebloods got injured and sometimes even killed. Blood status, be it pure, mixed, or dirty, did not grant immunity.
Lucius learned very early in his life the consequences of not carrying a wand with him when he was out with his father. The first time they were attacked by a group of Muggle-borns, all Lucius could do was to find a place to hide as quickly as possible, while also trying his best to dodge all the spells that the Muggle-borns were casting. It was clear that Abraxas was their main target, but they didn't seem to care at all about the presence of an entitled Pureblood child. The fact that Lucius could have easily been hit by one their spells did not matter to them. All they cared about was taking down some evil Purebloods.
Lucius was lucky that night, however. As small and as quick as he was, he was able to find a place to hide before the fighting got too intense. His father, meanwhile, bravely took down all the Muggle-borns.
Abraxas later put Lucius under the Cruciatus Curse for running and hiding like such a little coward. The fact that Lucius had not had a weapon to fight with did not matter to the Malfoy patriarch. Sometimes, being a Pureblood was not enough to protect you from another Pureblood.
Lucius learned one important lesson from that incident. He learned that whenever he went out, it was in his best interest to carry a weapon.
Lucius, therefore, started to carry with him the Malfoy family wand. It had been with the family since the first Malfoy, and each Malfoy since had carried and used it until they received their more personal wand for school.
Lucius, though, was still young and his magical education was still in the beginning stages. He did learn quickly, however, how to deflect spells. He also learned quickly how to make sure that none of the spells that he deflected accidentally hit his father. Lucius hated his father, but the young boy also knew that the Muggle-borns would kill him if Abraxas was brought down. As much as Lucius hated to admit it, he needed his father to protect him from the Muggle-borns.
All the attacks on him and his father motivated Lucius to learn, to learn how to fight and defend himself. Lucius was tired of just deflecting spells as he looked desperately for a hiding place. He was tired of being a little coward. He wanted to be brave like his father. He wanted to be able to fight. He wanted to be able to bring down the filthy Muggle-borns before they had the chance to bring him down.
Purebloods would reign supreme. Both Lucius's father and personal experience had taught the young Malfoy heir well.
In the eyes of Purebloods, Lucius eventually became the ultimate warrior. He became a Death Eater. He became one of those brave Purebloods that were willing to do whatever it took to eliminate the inferior, despicable Muggle-borns.
Those inferior, despicable Muggle-borns saw Lucius and those like him as monsters. In Lucius's eyes, though, the Muggle-borns were the monsters. They were the taint that was slowly but effectively killing the Wizarding World. The Muggle-borns, therefore, needed to be stopped before it was too late for the Purebloods.
For both sides, it was a matter of survival.
Most would say, however, that it was not that complex. The Muggle-borns were the victims, as they naturally made better victims than wealthy, privileged Purebloods did. It was, after all, a war between evil Purebloods and good Muggle-borns. There was no way that a Pureblood could ever be a victim. There was no way that a Pureblood could ever be a casualty of war.