Hey Capuga, I got the impression that Luther used the police firing on him to fake his death. It seemed like after losing Pete and his mom faking his death was the only way to save Petra.
Yeah he made comments about losing everyone close to him so he did that to save her.
He was trying to kill himself. The problem was that living is a hard habit to break, and he could ultimately not let himself die*. He subconsciously read the cop's body movements and moved so that he bullets didn't hit where they would actually kill him (this is actually what The Librarian did, consciously, when Luther's Mom tried to put a bullet in his head).
What he's trying to protect her from was, ultimately, him.
So, some making the sausage rambly from me. Likely to be prentious with a high chanc of boring for good measure.
The thing about his Mom dying was this: Ultimately, Luther is driven by the feelings of powerlessness, fear of becoming his father, and a somewhat irrational reaction to women being hurt, and his mother is at the top of his list. If you look back at every violent act Luther commits through the course of the series, he's reacting to the threat of a woman being hurt or insulted (or in the case of Vin, venting his anger at Petra being abused by her Dad on someone who deserves it:
He decks Jacobson when he talks about Petra.
He intervenes at the convenience store when a woman is threathened.
He gets involved when Vin is fighting with his girlfriend.
And so on. Luther himself doesn't realize this is a button, but the Librarian does, and the situation is designed to exploit that. He's trying to box Luther in by implicating him in the murders, and he's capitalizing on Luther's fears about Luther's mother getting hurt. So her dying by Luther's hand was very much part of the plan. It just that instead of going horribly wrong, the Librarian's plan went horribly right. He just didn't expect Luther to be quite so...er....talented.
Now, narratively, the way Luther's mind works, if his mother had survived, he would still have the most important thing in his world (and the second, in Petra) so to get the story and the character where he needed to go, her death was necessary. It's what finally broke him.
The long term implications of what this all means, from failing to die to believing he is death for anyone he could love to what comes after you've lost everything that ever matters, is sort of what Legend of Luther strode is about.
*And bullets could do the job. It's hard to kill students of the method, but not impossible.