Wages rose during the black death. Is this the Lump of Labor Fallacy?

The majority of economic research (from what I've seen anyway) shows that immigration doesn't depress native wages. To claim otherwise is called the "Lump of Labor fallacy." However, history textbooks claim that in Europe during the black death, around 30-50% of people died so wages went up because laborers were a lot more scarce. Wouldn't society consume 50% less if half the people died, so as a result only half as much labor would be needed?