Vaughan caught an elbow late on in the defeat at Carrow Road after Peter Odemwingie's early goal proved enough to give the Baggies their first Premier League win of the season.
The Nigerian capitalised on a mix-up between Ritchie de Laet and rookie keeper Declan Rudd, in for the suspended John Ruddy, to fire the Baggies ahead after three minutes.
Norwich, now without a victory in four league games, had a few half-chances but did not really test Ben Foster, and would have been out of contention with 15 minutes left but for a fine penalty save from Rudd.
However, in stoppage time Vaughan was flattened by a stray elbow from Gabriel Tamas at a corner, an incident which was missed by the referee, but could have brought a red card as well as a chance of redemption for the home side from the spot had it been seen as deliberate.
Vaughan came on as a second-half substitute having recovered from a knee injury picked up in pre-season following his summer move from Everton, but had to go off for treatment.
After the game, Lambert said: "James has gone to see the plastic surgeon at the minute, and it is a bad one. It has gone straight through the lip and they can't just stitch it up, the specialist has got to look at it.
"He had got a really nasty gash in his upper lip, which will need a bit of work on it.
"Hopefully we will sort it tonight, and we will have to see how he is."
Vaughan later revealed he did not suffer any serious damage.
The Norwich striker said on Twitter: "Plastic surgeon sorted me out. Think I will have 2 (sic) bite my lip over the 'incident' o wait already done that.
"Gutted we never got anything out of the game but we will keep working hard an the points will come."