Lee is in last place, behind Brewers third baseman Corey Hart, Mets third baseman David Wright, Phillies outfielder Pat Burrell and Giants outfielder Aaron Rowand.
The top three NL candidates each have accumulated nearly 4 million votes.
Rays third baseman Evan Longoria continues to hold off the charges of his closest two competitors in the American League, Jermaine Dye of the White Sox and Jason Giambi of the Yankees, as each has totaled more than 3.75 million votes.
Brian Roberts of the Orioles and Jose Guillen of the Royals round out the standings in fourth and fifth place, respectively.
The seventh annual Monster All-Star Game Final Vote ballot commenced exclusively on MLB.com at 2 p.m. CT on Sunday, and more than 33 million votes have been cast in the opening 72 hours of fan voting.
The online voting will continue until 4 p.m. CT on Thursday. In addition, fans again will be able to cast their votes via their mobile phones by texting the word "Vote" to 36197 to receive the Monster All-Star Game Final Vote candidates. In Canada, fans should text the word "Vote" to 88555.
Even if Lee doesn't win the Final Vote, he still has a chance to represent the Astros at the All-Star Game at Yankee Stadium next week. Cubs outfielder Alfonso Soriano is leaning toward attending the All-Star festivities, but he probably will not play. The left fielder has been sidelined since June 11, when he was hit by a pitch on his left hand and suffered a broken bone.
Lee would be a prime candidate to fill Soriano's spot. The decision rests with National League manager Clint Hurdle, skipper of the NL champion Rockies.
Alyson Footer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.