In a letter sent to CBS News Chairman and "60 Minutes" executive producer Jeff Fager, lawyer Elliot Peters said the May 22 segment about Armstrong was built on a series of falsehoods, and he accused the reputable CBS show of sloppy journalism.
"In the cold light of morning your story was either extraordinarily shoddy, to the point of being reckless and unprofessional, or a vicious hit-and-run job," Peters wrote. "In either case, a categorical on-air apology is required."
CBS News spokesman Kevin Tedesco said on Wednesday he couldn't immediately comment on the letter, but added: "We consider this the most thorough investigation into doping in the sport of cycling ever done."
Former teammate Tyler Hamilton alleged in the piece that Armstrong talked about using the banned blood-booster EPO to prepare for his third Tour de France in 2001 and cycling's governing body, the International Cycling Union, helped him hide a positive test at the Swiss event.
Last week, the head of Switzerland's anti-doping laboratory, Martial Saugy, denied allegations Armstrong tested positive for performing-enhancing drugs during the 2001 Tour de Suisse.
Saugy said his lab did find suspicious levels of EPO in four urine samples from the race Armstrong won, but he didn't know if any belonged to the seven-time Tour de France winner.
Armstrong has repeatedly denied doping and has never tested positive. Federal prosecutors in Los Angeles are investigating an alleged doping programme in Armstrong's teams.
"60 Minutes" also reported that the UCI officials brokered a meeting involving Armstrong and Saugy's World Anti-Doping Agency-accredited lab, which tested the Swiss race samples.
Saugy told the Swiss daily Neue Zurcher Zeitung last week that he met Armstrong and then-US Postal team manager Johan Bruyneel, but not in Lausanne as Hamilton claimed and unconnected to a suspicious test result.
Peters added the show's producers were alerted by Armstrong's camp prior to the show's airing that the Swiss-related allegations were false and provided evidence they say refuted them.
"What is particularly disturbing is that '60 Minutes' had access to the true facts, could easily have verified them, and apparently chose instead to broadcast untruths and then layer innuendo on top of the falsehoods," Peters said.
Armstrong has taken several steps to address the allegations made in the "60 Minutes" segment, posting a retort on Twitter, creating a website - facts4lance.com - and now urging CBS for an apology.
Last week, he also announced he was adding Peters and another high-profile attorney, John Keker, to his legal team.
