If we banned liars from holding office, they would have trouble finding enough candidates, Congress would lack a quorum, and the work of government would grind to a halt.
It doesn’t appear that any of his lies render him ineligible to hold office (e.g. lying about citizenship or residence, such as if he really is an illegal alien living in New Jersey). If he does a good job in Congress, the people who voted for him may be very forgiving; America has a long tradition of looking at one’s accomplishments rather than getting hung up over the past.