I know nothing about the comic Supergirl is based on or the themes it carried over from the comic aside from what I've seen folks mention, but I keep seeing stuff like how Lobo was cool but ultimately pointless as a character.
Lobo was actually very important to the movie as a foil to Kara in Ruthye's arc. He is not on the same level as them as a protagonist, but he needs to be established as a character early enough to give his presence some weight.
Because the real meat of his presence in the movie is his conversation with Ruthye where she says Krem killed her family for no reason, "for sport", and then Lobo calls that a reason. And then talks about how he kills for money. He's outright enthusiastic about the potential of her becoming a killer herself while Kara doesn't want that for her.
For Kara, no reason, not even revenge, is enough for Ruthye to carry the weight of taking a life, but for Lobo, who views sport or money as good enough of one no matter how superficial, revenge is definitely enough.
That's also why he was witness to the final scene with Krem. Because of what he represents in her arc, he needed to see Ruthye walk away from the path he wanted her to take and choose Kara's. And he needed to see Kara do the final blow because of what Kara represents: being good but not nice. She may take this life and carry that with her, but it still won't make her anything like him.
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