Yes, by "fan service" I meant something that the original dev does to improove the look of the characters, but that has no consequences on the story.
In Harem Hotel some outfit are "fan service", meaning their sole purpose is giving the player a better lewd experience in repeatable scenes, but if one decides not to buy them they can continue the story progression nonetheless.
Others are not only for looks, but are needed to progress the story (e.g. Maria's bartender outfit).
I think that the only ones that can break the game are those tied to the story progression... (also, I'm far for being a Ren'Py expert, so I could be wrong).
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Instead, if an outfit is "fan-made", yes: if you save with a character having an unofficial outfit, then remove the mod, that save won't work with the unmodded game.
But, if I've understood correctly, Lain's mod only contains fan-made scenes, not fan-made outfits.