If I just wanted a more formal/technical (to literary discussion) term for “story”, I’d probably go with narrative, or simply work, if I wanted to avoid bringing up discussion about whether the story is in fact a narrated thing. I would likely avoid lecture, since its most salient meaning in modern English is “reading/explaining something out loud to other people” (“my mom lectured me about my grades”, “the teacher lectured about chinese history”).
As for why there’s no word for “story” analogous to prologue/epilogue, all I can say is that English happens not to have a word of that sort. There are a myriad of ways that a language can derive a word for a concept, and English happens not to have derived a word from Greek -logue to refer to the story itself as opposed to the epilogue and prologue, like it did for prologue and epilogue themselves. Instead it uses a French borrowing story, or a Latinate borrowing narrative. You might as well ask why English doesn’t have a French loan for “invention” but instead has a Latinate one.