Actually Jed Bartlett defeated Lewis Eisenhower, who had been Lassiter's vice-president, Eisenhower is a cousin to the Dwight Eisenhower branch of the family, he came from Ohio, let's skip back first, Lassiter defeated Roland Pierce in the 1994 election in a Reaganesque/Nixonesque landslide.
Hold on. I'm pretty sure these things were never mentioned in the series. In fact, series never mentions things like a) Bartlet's 1998 opponent, b) exact Lassiter's time in office, c) exact Newman's term in office etc. etc.
So, from where are you getting these informations?