Lott lost his Majority Leader position because he woudn't defend his saying that the nation would have fared better with Thurmond winning the 1948 presidency.
He didn't put any other interpretation on those words than as a support of segregation. He "confessed" his former support of segregation in his following apologies.
Did he also "confess" his former membership in the Democrat party, which was contemporaneous with his support of segregation? Probably not.