The poll shows Lamont ahead 51-47 percent among likely voters in the Aug. 8 Democratic primary. That compares to a 55-40 percent lead for Lieberman in a similar poll in June.
The telephone survey of 2,502 registered voters was conducted July 13-18. It has a sampling error margin of about 2 percentage points. But the error margin among the 653 likely Democratic primary voters is 3.8 percentage points, putting the candidates in a statistical dead heat.
Lamont, a multimillionaire and founder of a cable television company that has wired college campuses, has contributed a total of $2.5 million to his own campaign.
He has gained national attention by challenging Lieberman, who has come under fire from some Democrats for his support of the war in Iraq and a perceived closeness with congressional Republicans and President Bush.
"More Democrats have a favorable opinion of Lamont, who was largely unknown last month, and see him as an acceptable alternative to Lieberman," said Quinnipiac University Poll Director Douglas Schwartz. "But Lieberman's strength among Republicans and independents gives him the lead in a three-way matchup in November."
Lieberman has said he will run as a third-party candidate in November should he lose the Democratic primary.
The poll shows him leading a three way race with the support of 51 percent of likely voters, compared to 27 percent for Lamont and 9 percent for Republican Alan Schlesinger.
"We think the voters of Connecticut are continuing to realize that Ned represents the kind of change they want in Wahshington," said Lamont campaign spokeswoman Liz Dupont-Diehl. "It's clear that Joe Lieberman is just interested in hanging on to power."
Lieberman campaign spokeswoman Marion Steinfels said the poll simply shows that the race is "competitive."
"We've been treating it that way, and we continue to work hard to make sure Joe Lieberman wins on Aug. 8," she said.
The campaign announced Thursday that former President Bill Clinton will be coming to Connecticut to campaign for Lieberman.
The two politicians have known each other since Clinton worked on Lieberman's first campaign for state Senate in 1970. Clinton was a student at Yale University at the time.
Clinton has defended Lieberman's position on the war in Iraq, saying he agrees with Lieberman that the U.S. should not set a strict timetable for withdrawing soldiers.
Clinton has also said he thinks it is wrong for Democrats to challenge one of their own.