A British parliamentary committee report published on Monday said Team Sky crossed an "ethical line" by using permitted medication to enhance the performance of Tour de France winner Bradley Wiggins.
It added that the widespread therapeutic use exemption (TUE) system was open to abuse.
Team Sky and Wiggins have both issued statements to "strongly refute" the report's conclusions.
Lappartient said the report had the power to affect the sport's credibility.
"We have the Cycling Anti-Doping Foundation, they have the power of investigation. I would like them to do this, to see if there is some violation of anti-doping rules," he told the BBC on Wednesday.
"They (Team Sky) had at the time the TUE agreement but now we have the evidence that it seems to be organised," added Lappartient.
"If you are using substances to increase your performances, I think this is exactly what is cheating."
Team Sky and Wiggins have denied using TUEs for anything other than medical need.
The government report, which said there was no violation of the World Anti-Doping Agency (WADA) code, also accused Sky and British Cycling of "serious, unprofessional and inexcusable" behaviour in failing to keep proper medical records.
Team Sky said they took full responsibility for mistakes made in areas where they had already acknowledged they fell short and Lappartient is concerned by the impact of the allegations on the sport's image.
"I read the press release from Team Sky say 'look we apologise, we recognise that we made some mistakes'. A mistake is something you've done without an intention to be wrong. The report is a little bit different," he said.
"It seems that it was a little bit organised, so it's maybe not a mistake but a fault, which is different, because that could affect the credibility globally of our sport and that's why I'm concerned about this."
Team Sky issued a statement in response to Lappartient's comments.
"Team Sky is happy to co-operate with any investigation by the UCI and we would welcome further scrutiny of the Select Committee's report," they said.
"While we have acknowledged past failings, we strongly deny the very serious new allegations about the use of medication to enhance performance, as does Bradley Wiggins."
Team Sky said they were concerned that the committee had presented "unsubstantiated allegations" without providing evidence to support them, which they said was "fundamentally unfair" to them and their riders.
"We welcome any review by the UCI which can help establish the nature of the evidence relied on by the Committee in coming to its conclusions," Team Sky said.
