US Anti-Doping Agency (USADA) chief Travis Tygart alleged last month that the Lausanne lab "tipped off" the US rider about the illegal blood booster erythropoietin (EPO) after a "suspicious" sample he gave following the 2001 Tour of Switzerland.
It was a USADA investigation that led to Armstrong, who has since admitted he was a serial dope cheat, being stripped of his seven Tour de France titles.
But Fahey, speaking in an interview with AFP after a London news conference on Tuesday, said WADA would not act on Tygart's allegations as they pre-dated the time when the global body had started to accredit testing facilities.
"No, he spoke about an event prior to the establishment of WADA (accreditation)," Fahey replied when asked by AFP if WADA, founded in 1999, would act on Tygart's allegations against the Swiss facility.
"Clearly we have certain rights in respect of accredited laboratories and the personnel within those laboratories in recent times," the Australian added.
"But he (Tygart) spoke about a time back in 2001 when there was no WADA in existence (as it is today)," Fahey said.
"We may have just been kicking off around that time so it's not relevant," he said.
"Was he accurate?
"I can't really add to what he's said.
"There have certainly been many stories of that time connected to Lance Armstrong and various other people who were relevant to samples he gave in the sport of cycling going back to the turn of the century.
"Those facts will, I believe, always have some level of conjecture attached
Fahey said he was not suggesting Tygart was wrong.
"I'm simply saying there's nothing there that allowed WADA to move on because it related to an alleged event at a time before we were accrediting laboratories."
Last month, Martial Saugy, head of the Lausanne laboratory, denied Tygart's claims by saying: "Did I give the keys to get around EPO tests? The answer is clear: no."