While I get why some viewers kinda think that the appearance by Lobo was kind of out of no where (aside from showing that that Brigands are a wider threat that people are understandably mad about to hire Lobo to go murder individual members of their gang), when he kinda acts as another point of view in the "experienced something horrific as a child" spectrum Clark, Kara, Ruthye and even Krem (in the original cut, more on that later) all exist on.
Like, with Clark while he's a survivor of Krypton's destruction just as much as Kara's family, due to his being too young to remember it and having grown up in Kansas with no exposure to Kryptonian society beyond some fragmented recordings from his bio!parents. As such, he's kind of emotionally insulated from it with his idyllic upbringing with the Kents meaning he's able to grow up a well adjusted, albeit wistful, person whose knowledge of his loss kinda comes to him second hand.
With Kara, however, while she was born after the destruction of Krypton, through her childhood to teen years she was able to experience decline of Argo City first hand, as over time her sense of normalcy was eroded until she was (potentially) the only person left. Experiencing the loss first-hand informs her behaviour as an adult, and while she's still a good person, she's carrying around a lot of survivor's guilt (among other things), which makes her disinclined to see other people go through what she had to.
With Ruthye, she reacts to the death of her family with the rather simplistic desire for a Vengeance Quest, and while the emotional pain is something recent and hurts, she is still able to recover from it through hanging out with Kara and still having extended family to stay with. The film, through Kara, is very clear about how Ruthye charging off with a sword she barely knows how to use isn't a construct way to move past her grief (not so implicitly calling out stories where an older person teachs a child to kill to get revenge, a la Leon: the Professional, in the process). In this case the emotional catharsis she thinks she'll get from killing Krem being outweighed with the potential emotional weight of killing someone as a child, in this instance.
With Krem, in earlier cuts of the film he went into his own backstory, albeit his monologues didn't survive until the final cut of the film, seemingly to lighten the tone? Anyway, Krem explains to Ruthye that just as he abuses people now, he was himself abused as a result of growing up in an all-male culture of human-trafficking space-pirates. However, Krem held the view that experiences and surviving this abuse made him a "stronger" person, much as how some folk who experienced violence as a child try to justify it by it toughening them up as they pass it on to the next generation. YMMV, if the film would have been included by keeping this in, although arguably within the narrative of the film his role doesn't exactly require nuance.
...And then there's Lobo, our final perspective. Lobo is the parody of the kind of person that Krem wants to be taken to ridiculous extremes. Grew up to be the final survivor of a race of tough, brawling space warriors? Lobo's not only that, he personally killed all the rest of his own species, so he is also the reason why he's the only one left (his daughter Crush excluded, if she exists in this continuity). Lobo has no trauma because he doesn't really have any interiority to him by design, he's something that happens to other people, rather than someone who experiences negative things. Within the context of the story (aside from being cool in small doses), Lobo is there provide a contrast to Kara by not really caring about Ruthye's emotional well being beyond "revenge is awesome!" because, again, Lobo is a parody character whose point of view isn't one we're meant to be taking seriously.
He's that quote from the Liam Neeson Naked Gun sequel,
“Once you kill a man for revenge there's no going back. A voice in your head is saying over and over, that was awesome!"
So, thematically, Lobo's there to indicate why Ruthye personally killing Krem is a bad idea, as the only way to do it without negative effects is either by already being so "damaged" that no longer impacts you OR being by being an emotionally stunted person who treats the universe like they're in GTA with only a loosely defined "code" to make it seem less overtly monstrous.
