We're a witch's cat, and we've been sent out to collect a flower for a spell our mistress is brewing up. Along the way, we could potentially die a lot.
Well, we're a cat and we have nine lives, so that's okay.
Structure-wise, the story takes a pretty narrow path from start to finish. Almost always, any one choice will offer us one option that will continue the story, while all the options kill us. The exceptions are a couple of branches which quickly converge again onto the main storyline. Not to worry, though: the death scenes take us right back to the choice that killed us, allowing us to choose a different option and, hopefully, live.
That's the focus or gimmick of the story, I think. It's even in the title, a pun derived from the word "lives": the verb, simple present tense of "to live", or the noun, plural of "life". It's interesting, but it doesn't appear to add anything to the story, aside from a hint of an excuse for how we're able to replay our choices. It's not as if we have a limit of how often we can pull this "back from the dead" act, and it's not as if the game explicitly states that we're actually doing that.
The story itself seems simple enough. It seems our mistress is at odds with another, younger witch, though it's not entirely clear why. She did call our mistress a "goody two-shoes" in one of the death scenes, so unless it's more thoroughly explained in one of the death scenes that I missed, it could just be your basic good-vs-evil thing. To be honest, it kind of feels like the story exists in service of the gimmick than the other way around, in spite of how lightly the gimmick touches on the story.
As a breakfast, it's the pastry platter at the coffee convention you just crashed: maybe you don't really care about the differences between a French press and a Bun-o-matic filter and you're just here for the pound cake and biscuits, but we all know why the pound cake and biscuits are here at all.