I kind of doubt that what Im going to suggest is the real reason for V going off to do Phantom Liberty. I don't have faith that CDPR will make a thoughtful way to tie in the expansion with the main story. Hopefully I'm wrong, but based on what I've experienced so far with the patches, etc., just doesn't seem very wise in thinking so. Anyways.
What if there was something personal about Phantom Liberty, maybe a one-time chance thing? Doesn't even necessary have to involve trying to trick V into doing it for some miracle cure, maybe it was just something V needed done before they died, and this would be the one chance to do it. Maybe someone from V's past life comes in asking for a hand, or maybe V wants a chance for revenge. Die with no regrets, etc. And maybe it just has to do something with Militech, idk. Again, you'd have to balance it in a way that is both open enough to make sense with lifepaths, character stories, etc. but still tight enough to make a well rounded story. I think going in with "an old friend now part of Militech" way could make sense, everyone in NC makes a bunch of different friends. And maybe give that player customisation in their interactions with their friend, whether it ends with helping them with this last job or shooting them dead. Idk, but gives something personal for good story while kinda making sense within the timeline of the main game.