SCOTUS Justice Samuel Chase was impeached though not convicted by the Senate. Here is a list of federal judges investigated for impeachment, and a list of federal officials impeached. The first federal judge to be removed from office was John Pickering, and the most recent is Thomas Porteous. Only Congress has the power to impeach: SCOTUS cannot review an impeachment, and the presidential pardon power does not extend to impeachments.
Article 3, Section 1 of the Constitution states that "... The Judges, both of the supreme and inferior Courts, shall hold their Offices during good Behaviour..."; Article 1, Section 2, Clause 5 says "The House of Representatives ...shall have the sole Power of Impeachment", and Article 1, Section 3, Clauses 6 says "The Senate shall have the sole Power to try all Impeachments". The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors. Article 2, Section 4 says "The President, Vice President and all civil officers of the United States, shall be removed from office on impeachment for, and conviction of, treason, bribery, or other high crimes and misdemeanors".
Taken together, one might think that a civil officer can only be removed for criminal conduct while in office. This is by no means guaranteed, since it does not say that explicitly, and it is up to the Senate to determine whether, for example, lying during a confirmation hearing about previous conduct would satisfy the requirements of Article 2, Section 4. In order for them to make that determination, the House would have had to also previously decided that the alleged situation does constitute the conditions in that clause, since an official has to be both impeached and convicted, involving both houses. The conviction furthermore requires a 2/3 majority of the Senate ("no Person shall be convicted without the Concurrence of two thirds of the Members present").