What drove Lucifer to commiting such a deed?

Question

It’s easy to forget, but as the Lucifer episode "Monster" mentions, Lucifer isn’t a killer. He punishes, but in Hell everyone he punished was already dead. As DevilCop, he loves the idea of the wicked being punished -- and he has no problem supporting humans taking matters into their own hands -- but he himself doesn’t go around killing people. He’s not a soldier like Amenadiel, and he’s clearly not as much of a zealot as Uriel was.

So to go from that to straight up killing his own brother, no matter how justified it was, is a big step for Lucifer and one that of course sends him into a spiral. It means so much that the typical Lucifer distraction mechanisms, the acting out and the partying, don’t even look fun this time around. He’s drinking non-stop and hooking up with women (even at crime scenes), which he’s done a million times and will do a million times more, but even he doesn’t look as into it anymore. And that’s long before he plays sad piano or “sees” Uriel around. This is Lucifer in his time of grieving...

How can this happen to an angel? Especially, the devil in flesh, Lucifer Morningstar! Why did he kill his brother? He is an angel, not a demon! Was it a brother's revenge, for Chloe's protection or even for Maze's protection? This episode can be a bit confusing and I'm open to your explanations!

Answer 1

I think it's obvious from Lucifer's reaction that killing Uriel was a spontaneous, and ultimately bad, choice that Lucifer made. His brother's actions kept escalating out of control until Lucifer, in what lawyers would call "the heat of the moment", made a snap judgement call to kill Uriel.

It's important to note that Lucifer largely stayed out of the fight, at first; Uriel not only fought off Lucifer and a de-powered Amenadiel, but he had beating Mazikeen nearly unconscious as well. In the end, though, the thing that pushed Lucifer over the edge was Uriel's threat to Chloe:

URIEL: Because you made it so difficult, now I'm gonna take out mom and the detective. You can't stop me, brother.

At this point Lucifer had no other way to save Chloe's life but to stop Uriel, and since neither he nor Amenadiel nor Maze could fight Uriel directly, Lucifer had to kill him.

But it's equally important to note that Lucifer was immediately shocked and upset at what he'd done. He genuinely seems to regret his actions (something he has rarely been shown to do in the past), which implies that he didn't spend any time "thinking" about it. He just did it, and now he's going to suffer for it.

Answer 2

So long story short:
Lucifer made a decision without thinking it through. At first he was just trying to get rid of Uriel and protect Chloe and their mother (goddess). This is a decision that shows compassion for the detective and their supposedly evil mother.
Of course Lucifer doesn't consider himself as a killer but he did commit "manslaughter" which is still murder.
Lucifer never intentionally meant to kill Uriel, and even if he did it was for the protection of family and lovely friend (with benefits). Even if it was out of anger. Lucifer is relatively speaking, "a good person."