A day after Froome showed a rare sign of weakness on the final slope, Team Sky sent Mikel Landa in front when twice champion Alberto Contador attacked early on, forcing his other rivals to chase as the Spaniard became a threat for the overall title.
Froome and team mate Michal Kwiatkowski contributed to the chase later in the stage to make sure the Briton would stay ahead of Landa in the general classification.
"It's not the perfect plan for Sky to have Chris Froome attacking and chasing against Landa," said Le Mond.
"There is something else going on," he added, referring to the fact that Landa's contract expires at the end of the season.
On Thursday, Landa and sports director Nicolas Portal was seen arguing after the Spaniard finished 17 seconds ahead of his leader in Peyragudes as Froome cracked in the final 200 metres.
"There was a problem after yesterday's stage and I thought it was crazy because Landa rode Chris up to 200 metres from the finish," said LeMond, who won the Tour in 1986, 1989 and 1990.
Sky, however, can play the Landa card again as he is fifth overall, 1:09 behind race leader Fabio Aru, and both Landa and Froome could work as a double act.
"My perspective as a racer is that they are covering up something, make it like it was a planned strategy and that there is no friction," LeMond said.
"Landa dedicated himself to the team yesterday and he was criticised or talked down."
Should Landa be loyal or go for it if he fancies his chances?
"In 1985, I made the mistake of being loyal and nobody paid me back," said LeMond.
In 1985, although he was possibly as strong as his leader, LeMond was riding in support of Bernard Hinault, who promised he would help the American win the following year.
The Frenchman failed to deliver and raced against LeMond, who did nevertheless prevail in the end.
But Landa's contract could mean he has to help Froome, who was in a similar position in 2012 when he seemed stronger in the mountains than Sky team mate and eventual champion Bradley Wiggins, all the way to Paris.
"It depends on his contract. It depends what he agreed to, most likely that he is a lieutenant for Chris Froome and if that's the case he should be loyal," said LeMond.