Why didn’t Lily just disapparate with Harry ?

Same as the title; I have always wondered why Lily (and for that matter James as well) not just disapparate with Harry, when Voldemort had appeared to their doorstep. I can understand that James didn’t get a head-start, but Lily did… The protection that was bestowed upon harry had to have been accidental on her part, right ? Surely she didn’t know that that’s what will happen….then isn’t disapparating the more logical thing to do ? And Lily was no ordinary witch, she was highly gifted and had been thwarting Voldemort’s attempts at murder since a while, her reflexes were surely sharp enough.. Has JKR ever given an explanation for this ?