Regarding Lerner's appearance, I cannot say if she has waived her Fifth Amendment right or not. I know that in civil cases and in front of a grand jury, a witness is not normally allowed not to testify at all. They must invoke their Fifth Amendment right to individual questions. In civil cases, the fact finder can draw adverse inferences on the witness's refusal to answer questions.
At criminal trials, they are not usually allowed to testify at all if they are going to invoke their Fifth Amendment right to some of the questions because it is simply unfair to both parties to get only part of the story. At least I think that is the rationale as I have never seen a witness take the stand knowing he or she is going to take the Fifth.
If I'm not mistaken, one doesn't have to be under oath to be guilty of misleading or obstructing Congress. I believe that Lt.Col. Oliver North had made unsworn statements to members outside of committee meetings which misled them in their duties. He was convicted of obstruction of Congress but that conviction was vacated because of an unrelated foul up.