What is the meaning of the serpent’s claim that the woman would not “surely” or “certainly” die (Gen 3:4)?

Literally, the Hebrew says something like “Dying, you will not die,” which is an instance of the Hebrew use of repetition for the sake of emphasis. That being the case, there are two things the serpent might mean: first, that it is certain that they would not die (here the certainty attaches to the whole claim); second, that it is not certain whether or not they would die (here there is simply a denial that the consequence was certain). Naturally, the first is the much stronger claim, and amounts to a positive claim that Eve would remain immortal even after eating; both claims are lies, but the first is a much worse lie. Still, even if the second claim, “Maybe you won’t die after all,” is the one meant, the lie is terrible, because it invites Eve to take a risk for the forbidden fruit.