If she made even one visit to the WH there would have been some email traffic simply to arrange the meeting, confirm it, and provide clearance information to actually visit the WH. I don’t know the answer - but confirming any visits by her to the WH would be damning evidence.
Lerner admitted that she had made dozens of visits in the time frame in question to the WH. WH logs if I recall gave it away.
Email coded with one of the oldest and most unbreakable codes ever devised, they are called a book code and have been used for hundreds of years. Why email, why not just a letter?