There's no reason why it could change the sound but not the vision to a listener who cares about the lip movements. You see, the Babel fish isn't like a headphone, it doesn't just whisper the translation to your ear. Let me quote The Hitch Hiker's Guide to the Galaxy chapter 6.
‘The Babel fish,’ said The Hitch Hiker's Guide to the Galaxy quietly, ‘is small, yellow and leech-like, and probabliy the oddest thing in the Universe. It feeds on brainwave energy to nourish itself with. It then excretes into the mind of its carrier a telepathic matrix formed by combining the conscious thought frequencies with nerve signals picked up from the speech centres of the brain which has supplied them. The practical upshot of all this is that if you stick a Babel fish in your ear you can instantly understand anything said to you in any language. The speech patterns you actually hear decode the brainwave matrix which has been fed into your mind by your Babel fish.[’]
Also, let me quote chapter 5 for the description of what using a Babel fish felt like to Arthur. Note that at that time he was listening to a loudspeaker without seeing the Vogon captain, so there was no way to see the lips.
He was still listening to the howling gargles, he knew that, only now it had somehow taken on the semblance of perfectly straight-forward English.
From this, I think the Babel fish simply gives you the meaning of the Vogon speech, and it's your brain that creates the illusion of the sound of English words or the lip movements for them. That experience would be impossible to show in a movie with current technology, so the movie simply shows the Vogon speaking English.