Both judges are suspected in a large-scale judicial corruption probe.
The resolution to remove Lauzikas from office was passed in a secret ballot with 49 votes in favor, seven against and nine abstentions.
The resolution on Bavejanas was adopted in a vote of 53 to three with eight abstentions.
Both judges were temporarily suspended from duty until now.
MP Vytautas Bakas said before Tuesday's vote that the motion to dismiss the judges, rather than initiating impeachment procedures against them, run counter to the Constitution.
Under the Constitution, Supreme Court judges are appointed and dismissed by the Seimas. Court of Appeals judges are appointed and dismissed by the president, subject to the parliament's approval.
A total of 48 people are suspected of various corruption crimes in the high-profile probe.