In papers filed in U.S. District Court in Washington, Armstrong's lawyers asked a judge to dismiss the lawsuit Landis filed under a federal law that allows whistle-blowers to report fraud in exchange for a reward.
The once-revered athlete is fighting to hang on to what remains of his reputation after he was stripped last year of his seven Tour de France titles and banned for life from cycling.
Armstrong, who admitted to doping in January, faced a separate deadline on Tuesday to respond to the U.S. Justice Department's decision to join Landis' lawsuit.
The lawsuit centres around sponsorship money from the U.S. Postal Service, which paid $40 million (26 million pounds) from 1998 through 2004 to have Armstrong and his teammates from Tailwind Sports wear its logo during record-breaking wins.
In February, the Justice Department said the sponsorship contract included promises to obey cycling rules. It said those rules were broken. It is asking for triple damages.
Armstrong's lawyer Robert Luskin has said that the Postal Service benefited from the sponsorship, regardless of doping.
The False Claims Act allows whistle-blowers to sue over suspected fraud involving government money, and, if successful, get a percentage of whatever the government recovers.
In asking for Landis' 2010 suit to be dismissed, Armstrong's lawyers pointed to Landis' own earlier denials of doping.
"Now he would like to be paid for casting the first stone," they wrote.
Landis' lawyer Paul Scott has said previously that Armstrong's "false victories" forever hurt the Postal Service.
(Reporting by David Ingram; Editing by Eric Walsh and Eric Beech)
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