Lerner had an attorney. A very expensive attorney. Questions like that is what they are for.
Either:
a.) he was caught unaware by her opening statement.
or b.) they are willingly following a political defense via the media as opposed to a legal defense via the law.
Further, employment of the 5th Amendment isn't rocket science. I took Civics in the 8th grade...and our textbook addressed this very question. At one time, it was what is called "common knowledge".
I've come to regard Congressional hearings as largely political theater, since Congress feels free to make up the rules as it goes along. Certainly a criminal defendant is allowed to make public statements to the media without waiving Fifth Amendment rights; the main case where statements without waiver may be restricted is before the jury (since jurors are not expected to be able to forget such statements).
Personally, I think one of the most important things that should be done to curb Fifth Amendment abuse by public officials is to make clear that federal employees' duties includes testifying regarding their actions on the job; while the Fifth Amendment applies to federal employees as it does to anyone else, refusal to testify about what one was doing on one's job should be regarded as a refusal to do one's job (i.e. a basis for immediate dismissal).