I think I remember that Lerner made roughly 50 visits to the WH during the time of the persecution of tea party organizations and their ilk. Why would you committ to paper or electrons anything that could be traced? Wouldn’t face to face, unrecorded conversations be safer? I think the Mafia uses this tactic.
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.