Let's check the source, the Fifth Amendment:
"...[No person] shall be compelled in any criminal case to be a witness against himself, ..."
I don't see anything here which states that you must remain completely silent in order to have a Fifth Amendment right not to be compelled to testify against one's self.
These same legal tyrants who would claim so, will also claim that you must identify yourself, for example; that is, they compel you to speak and would not hesitate to charge you for obstruction if you claimed an identity not your own. THAT is the very essence of requiring one to testify against one's self.
Lerner said she did nothing wrong and evidently said so under oath(?). If so, then the proper charge is perjury if it can be proved that she did do something wrong and intentionally lied about it.
Without unconditional immunity which applies in every jurisdiction in the world, there should be no way to punish someone for failing to testify. Then there are further complications which apply to privileged communications with one's spouse, doctor, priest, or lawyer.
But apparently there is a long standing court tradition that if you start answering questions you waive your right to the fifth. And supposedly that's to protect the right to cross examine. You can't present one side in court and then shut down when the opposing attorneys start questioning.
That's what Issa and committee are trying to apply here, basically claiming that the congressional hearing is a court and the same rules apply.
But I disagree. Unless she's been indicted and it's clearly a trial, then I think she can refuse.