While not impossible (Dodgson didn’t die till after the advent of sound recording), I was skeptical when this blog 22 Words claimed to have a recording of “Lewis Carroll reading ‘Jabberwocky.'” But I see they updated it with the comment “Oops! Sorry…This isn’t Lewis Carroll reading. Not sure how I made that mistake…” I can guess how they made the mistake: they had embedded the sound only from this strange YouTube animation. Its creator, Jim Clark, explains himself thusly: “Here is a virtual movie of Lewis Carroll reading his much loved poem Jabberwocky. The poem is read superbly by Justin Brett.”
There’s no known voice recordings of Carroll are there?