The first time might not be in a World Cup race, though. Max Gartner says he's been talking to Vonn's sponsor Red Bull.
"We're working on some plans, but we do hope this will happen down the road," Gartner says. "We do hope it will happen in Lake Louise.
"It's the best venue where men and women have an equal amount of time on the slopes."
Vonn asked FIS, the world governing body of skiing, if she could race in the men's World Cup downhill and super-G this weekend at Lake Louise.
The reigning Olympic champion has dominated women's races at the mountain with 11 World Cup victories and 17 podiums in total.
But FIS denied her request earlier this month so emphatically there seemed no chance of a change in attitude.
An exhibition event, with a lot of prize money tempting the world's top male and female racers to participate, could be a step in that direction.
"Her racing the men, I was a big proponent of that and I still haven't given up the fact that's going to happen one day," Gartner says.
"We've had some discussions with Red Bull already. We would like to see this happen at some point. We're not giving up on that plan and from what I hear from Lindsey, she's not giving up on the plan either."
The first of three training runs for Saturday's season-opening downhill ran Wednesday at Lake Louise. Had Vonn been allowed to race the men, there would have been a media army for the opening training run instead of a handful of journalists.
Austrians Max Franz and defending World Cup downhill champion Klaus Kroell finished first and second respectively in soft snow. Adrien Theaux of France was third. Erik Guay of Mont-Tremblant, Que., was the top Canadian in fourth.
From the men, there was a cross-section of opinions on whether Vonn should race men and how she would fare against them at Lake Louise this weekend.
The women's downhill course is 106 metres shorter in length than the men's with 47 metres less in vertical drop, but the tracks are otherwise identical.
Vonn won one of her two downhills at Lake Louise in 2011 in a time of one minute 51.35 seconds. The winning time in the men's race, on a longer course, was 1:47.28.
Kroell didn't think Vonn could finish above 30th at Lake Louise.
"I don't think so," he said. "It's a very close race every year and the speed is much higher than in the women's race. I think she will lose some seconds on us."
Norway's Aksel Lund Svindal, winner of the super-G at Lake Louise last year, gives Vonn a better chance at a top-30 result.
"I've trained with her. My experience is if you are on a hill that she likes and you don't ski good, she can beat you," he said. "It's realistic that she would be in the race."
There was more consensus among the men on a marketing opportunity missed, as Vonn's presence this weekend would have given the sport a heightened profile in North America, particularly in the United States.
"I say let her race," Svindal said. "To get America more involved in skiing would be good for us. From a marketing point of view, it seems very strange to just cut it off like that and say 'not possible.'
"If I was FIS, I would keep that door open. Those are the kind of stories that are bigger than the sport and the kind of stories that would be popular in America."
Vancouver's Manuel Osborne-Paradis was less enthusiastic on the idea of racing Vonn in a World Cup, but said he would in a separate event.
"It's something she wants to prove. I don't think World Cup is the right place to prove this," he said.
"I know Red Bull has tossed around maybe having their own event. I would be more than happy to compete with men and women and whoever else they want to have at them. But at the World Cup, this is our livelihood.
"Start numbers mean a whole lot. Hypothetically, if she falls and she's in the (safety) net for an hour, she's ruined everybody's race behind her. They have no chance of catching the other guys. With 10 races, that's 10 per cent of your season gone."
Guay pointed to Annika Sorenstam teeing off in a PGA tournament in 2003 and goaltender Manon Rheaume appearing in exhibition games for the NHL's Tampa Bay Lightning in 1992 and 1993 as significant moments in those sports.
"If the PGA can do it and the NHL can do it, why not alpine skiing?" he asked. "Those are much bigger sports than ours and quite frankly we need the attention here in North America.
"There's 330 million people in the States and we need those viewers."
Ben Thomsen of Invermere, B.C., was 15th and Calgary's Jan Hudec was 19th in training. John Kucera of Calgary and Osborne-Paradis, both making comebacks from long-term injuries, were 48th and 54th respectively.
The brothers Conrad and Morgan Pridy of Whistler, B.C., were 62nd and 63rd. Jeffrey Frisch of Mont-Tremblant, Que., was 69th. A second training run is scheduled for Thursday.