I had a look at Wikipedia to see what kind of Experience Lieberman replaced in the Senate.
Weicker's tense relations with establishment Republicans may have roots in receiving strong support from President Nixon in his 1970 senate bid, support repaid in the eyes of his critics by a vehement attack on the White House while serving on the Watergate Committee. Later, his relations with the Bush family soured, and the brother of then Vice President Bush (Prescott Bush, Jr.) made a short-lived bid against Weicker to gain the 1982 Republican senate nomination. Finally, conservative animus spilled into overt support for Joe Lieberman in 1988, both from national sources such as National Review (publisher William F. Buckley, Jr., and his brother, former New York Senator James Buckley, both endorsed and campaigned for Lieberman in 1988), but more importantly, from rank-and-file Connecticut Republicans irate with Weicker's effort to make the local party more liberal and prevent the nomination of conservatives to state office, and the poor showing of Weicker-backed candidates in the 1986 elections. Weicker was defeated in the 1988 election by less than 1% of the vote, owing in large part to defections by Republicans to Lieberman.
Thank you, Lieberman, for representing Republican interests since 1988. Now please go away.