Options Trading: BS Implied Volatility under Normal returns

"Black-Scholes volatility" and "lognormal volatility" are two words for the same thing.  So the answer to your question is yes.This is practically a tautology, though.  The lognormal implied vol is whatever vol gives the right option price.  If you use that vol to compute anything else -- e.g., a delta hedge -- it will likely not be too far wrong but will contain modeling artifacts that arise from your assumptions.For example, in a world of normal prices, an ATM option always has [math]\delta=1/2[/math].  The lognormal model will give [math]\delta>1/2[/math] for the call, because it thinks that an upward move in price will also cause larger moves in future (adding to the option's value).