Well, without more specific information about this 'gekijouban bungaku shoujo light novel', it's hard to give a detailed account. It could potentially be a light novel that has something to do with a literary girl in a certain theater - related (gekijouban) context. Maybe it features a story centered around a girl who loves literature and the events that unfold in a particular setting, perhaps related to a theater or some kind of performance space.
Since I don't know much about 'gekijouban bungaku shoujo light novel', I can only make some general speculations. The 'bungaku shoujo' part might imply that the main character is a girl with a passion for literature. And the 'gekijouban' could be related to a special edition or something related to a theater. It could be a story full of literary references, with the girl's love for books and literature driving the plot, and the 'gekijouban' aspect adding some unique elements to the story, like a special performance or event that ties in with the literary theme.
I'm sorry, I'm not very familiar with 'gekijouban bungaku shoujo light novel'. It might be a relatively niche or region - specific work. You could try to search for it in some specialized light novel databases or forums.