Lee's fellow Republican who tested positive, Thom Tillis, appeared remotely.
Graham shrugged off calls for mandatory testing or tracing of senators or staff, saying: "You make it as safe as possible, you manage the risk and you go to work."
Democrats and their presidential candidate Joe Biden are demanding the Supreme Court nomination be left until after the election.
But Trump, trailing Biden in polls and returning to the campaign trail Monday night less than two weeks after falling ill with Covid-19, is desperate for a swift confirmation.
Graham said a final vote on Amy Coney Barrett's appointment could come as soon as October 22.
Amy Coney Barrett, a practicing Catholic, is well regarded by conservative Christians, who share many of her values including opposition to abortion and same-sex marriage.
Read also: Past Writings Indicate Amy Coney Barrett May Reverse Roe v. Wade
Trump's Supreme Court nominee, known for her finely honed legal arguments, vowed to apply the law apolitically and keep her faith and legal judgment separate.
"The policy decisions and value judgments of government must be made by the political branches elected by and accountable to the people," Barrett said at Monday's hearing.
"The public should not expect courts to do so, and courts should not try."