Nautilus is an interesting character who in no small way represents one side of the deep ocean in contrast to Nami, where Nami represents the wonder and beauty that can be found in the depths, while Nautilus represents the horror and terror of such a place.
Over all I feel like Nautilus's connection to the Shadow Isles should be a completely non existent one because his transformation from human to literal titan introduced a unique power and a different kind of threat that never really got much exposure: that there's something scary down in the depths of the oceans of Runeterra. It's not Void related (maybe) and it's not Shadow Isles related (maybe), it's something far more ancient, something primordial and impossible to comprehend; a force that's remained unchanged by the wars and shifting eras of the surface world, but is perhaps more terrifying than anything from those ages.
His powers could also be in stark contrast to Illaoi's culture and how the ocean is seen. Perhaps the dark goop that took Nautilus as a man is something that parellels or is in conflict with the great cycle represented by Nagakabouros and her children. The people of the Isles would probably not just look at Nautilus as a monster, but also an affront to their own beliefs and an enemy that must be destroyed. In Bilgewater that may not be the case but the native people probably never looked at Nautilus with anything but contempt and fear.
In Bilgewater Nautilus is probably a folk tale right about now, talked about in hushed tones and sung in tall tales in bars. Whether he's old or new isn't really relevent; he's gonna be a cultural figure regardless of how long he's been a part of Bilgewater's history.
With that in mind I feel like Nautilus's drive from revenge is not only him trying to relcaim his own sense of humanity but also avoiding his new nature as a monster of the deeps. Pursuing this goal is the only thing that connects him to his old life, and if he lets it go then what is he? That's the last vestige of humanity he has in a way and not having that drive is scary because all of a sudden he IS the monster people think he is, which is perhaps the scariest thing of all. In defending Bilgewater from the Harrowing he might also have another lease on that humanity; to serve as an eternal guardian of his former home. Maybe people won't like him and will fear him, but he'll keep the darkness at bay for as long as he remains standing.
''When consumed by utter darkness, there is nothing left but forward.''
I feel this line is core to Nautilus as a whole. If you boil it down, going forward is all Nautilus wants and needs. Forward to not be bogged down by the reality of who he is. Forward to push past the hatred and fear of people he may have once knew. Forward to escape the horror's he's witnessed and keep himself away from the depths. With that in mind I feel like he and Nami could find common ground once they got past the fact that they kinda embody exactly what the other wouldn't really like about their life and current situation. Nami's in a totally new world and has no clue where to go, but then she meets Nautilus and learns the nature of "Just keep going forward and you'll get somewhere eventually." Conversely Nautilus could see Nami's determination to protect her loved ones as inspiration to keep Bilgewater safe; she defied pre-destined events to be the hero her people NEEDED. Bilgewater NEEDS a protector, and regardless of what the people think Nautilus may just be the most qualified to take on such a task.
A friendship between the two is something I'd love to see, but as I said before, they kinda embody some really nasty things about the other's life; to Nami, Nautilus is the literal embodiment of both the horrors of the human world she has to face, and the deep ocean that threatens her people's existence. To Nautilus, Nami is the embodiment of the alure and terror of the deep ocean, given voice, will and obvious intent. Could they ever work past that to see each other as allies, and potentially comrades? I'd love to see it.
I'd also like to see both Nami and Nautilus save Bilgewater from a Harrowing some day. That'd be sick.
That was a real jumble there but hopefully someone found it coherent.