Thou shalt not murder.
It is doctrinally unfeasible to do that and expect Heaven especially if the drive is revenge rather than defense.
There are degrees of murder, and murder=/=killing. Had the state executed this man (he was sentenced to death for murdering the little girl) it would have been perfectly moral under Catholic teaching. That sentence was commuted in a way that I'd argue was unjust - he got off for one of the most heinous crimes imaginable because he was rich and had connections. Was his vigilante killing a sin? Absolutely. Was it as grave as the sin that Frank himself committed? Absolutely not.
I would say I hope they repent but are the guys that did it still alive?
This was in the early 1900s so the chances are slim. I doubt any of them were Catholic in any case - there was considerably more anti-Catholic statement in the South at the time than there was anti-semitism, with only 0.4% of Georgia's population being practicing Catholics around the time of the Civil War. For example, the first practicing Jewish senator in the US was Judah P. Benjamin of Louisiana, who later served in the Confederate Cabinet. The first Jewish senator by ancestry was David Levy Yulee of Florida, who was another defender of slavery. The South is a lot more complicated than people make it out to be,
How do you know it was not the Black man btw?
I just copy-pasted the details of the murder from Wikipedia:
Around noon on April 26, she went to the factory to claim her pay. The next day, shortly before 3:00 a.m., the factory's night watchman, Newt Lee, went to the factory basement to use the toilet.
[36] After leaving the toilet, Lee discovered Phagan's body in the rear of the basement near an incinerator and called the police.
Her dress was up around her waist and a strip from her petticoat had been torn off and wrapped around her neck. Her face was blackened and scratched, and her head was bruised and battered. A 7-foot (2.1 m) strip of 1⁄4-inch (6.4 mm) wrapping cord was tied into a loop around her neck, buried 1⁄4 in (6.4 mm) deep, showing that she had been strangled. Her underwear was still around her hips, but stained with blood and torn open. Her skin was covered with ashes and dirt from the floor, initially making it appear to first responding officers that she and her assailant had struggled in the basement.
[37]'
A service ramp at the rear of the basement led to a sliding door that opened into an alley; the police found the door had been tampered with so it could be opened without unlocking it. Later examination found bloody fingerprints on the door, as well as a metal pipe that had been used as a crowbar.
[38] Some evidence at the crime scene was improperly handled by the police investigators: a trail in the dirt (from the elevator shaft) along which police believed Phagan had been dragged was trampled; the footprints were never identified.
[39]Two notes were found in a pile of rubbish by Phagan's head, and became known as the "murder notes". One said: "he said he wood love me land down play like the night witch did it but that long tall black negro did boy his slef." The other said, "mam that negro hire down here did this i went to make water and he push me down that hole a long tall negro black that hoo it wase long sleam tall negro i write while play with me." The phrase "night witch" was thought to mean "night watch[man]"; when the notes were initially read aloud, Lee, who was black, said: "Boss, it looks like they are trying to lay it on me."
[n 7] Lee was arrested that morning based on these notes and his apparent familiarity with the body – he stated that the girl was white, when the police, because of the filth and darkness in the basement, initially thought she was black. A trail leading back to the elevator suggested to police that the body had been moved by Lee.
The main issue with the theory that either black man did it is that blood and hair were found on the second floor of the factory, near Frank's office. Phagan had been laid off and had returned to the factory to get her last paycheck, so it would make sense that she would go to her former boss's office. It appeared as if the girl had been murdered on the second floor and then moved later. Frank acted incredibly suspicious and nervous when first interviewed and at several critical points during the investigation as new evidence emerged. Frank hired Pinkertons to try and push the blame off to other suspects. Employees related a pattern of sexual harassment and unwanted advancements by Frank. A bloody shirt was found in a burn barrel at Newt Lee's residence; the first black man they tried to pin this on and the night watchman who discovered the body. The problem was that Lee was illiterate and could not have written the notes, and the blood on the shirt was smeared all the way up into the armpits, which made the police suspicious as that's apparently not typical in a shirt which is bloodied while wearing it, suggesting a plant by the shady private detectives whom Frank had hired.
They then tried to pin the blame on another black man, Jim Conley, who admitted to having written the two notes, but claimed that Frank had dictated the notes to him and paid him in cigarettes and was also acting suspicious, changing his story multiple times. The police were uneasy about this element and tried to arrange a meeting in in which both men were present to get to the bottom of their conflicting claims. Conley agreed, but Frank refused to meet. Conley was eventually arrested as an accomplice, having confessed to helping Frank move the body and to writing the notes for $200 dollars, claiming that Frank had asked him to take the body to the basement and burn it in the incinerator which it was found near.
In the trial Frank's defense called mostly people who were currently working for him to testify as to his character, with the obvious issue that they depended on his good will for their livelihoods. Conley was cross-examined for 16 hours without folding, and the frustrated defense tried to have his testimony struck from the record after they failed to break him.
I think that it's critical to the case to understand who the Pinkertons were. These were hired thugs essentially, who were hired at the time by wealthy factory owners to intimidate and control their workers, primarily by stopping them from unionizing and asking for better conditions and by breaking strikes. I don't think it's a coincidence that after hiring them a large amount of testimony began to flow from current workers that contradicted those people who had come forth with allegations of sexual harassment and suspicious activity on the day of the murder. I think that the ADL-sponsored narrative that the people of Atlanta (including the Jews on the jury!) were consumed with mad, ravenous antisemitism is flat-out ludicrous. I think it's far more likely that they saw a rich factory owner trying to buy his way out of justice by hiring private investigators and attempting desperately to frame other people for the murder.