Assuming lognormal prices is convenient and partly sensible: it prevents negative prices and makes percentage moves symmetric. It also produces thin tails, continuous paths and constant volatility, none of which describe an equity market on a bad morning.
Every visible distortion of the volatility-surface is the market correcting for this. volatility-skew exists because traders know downside jumps are more likely than the model allows, and they pay up for the strikes the model considers nearly impossible.
Example: with XYZ at $50 and 25% implied volatility, a lognormal model puts the 30-day chance of a close below $40 at well under 1%. Actual equity history says gaps of that size happen often enough that the $40 put will never trade at the model's price.
Related: black-scholes-assumptions, volatility-skew, tail-risk, standard-deviation-move