With NO traffic it takes me 15 minutes from 20th Avenue on the Whitestone expressway (about 1 mile from the VW expway cutoff) to get to JFK. I don't see how it could take only 3 minutes more from Ft. Lee and go through security.
He (jg7124) probably mean's Fort Lee to LGA in 18 minutes. Very doable, at the right time of day if you park in the garage.