Lyon are by far the most successful club in the competition's history, but they lost to Chelsea on penalties to crash out at the quarter-final stage last season, and Horan and her team are keen to make up for that disappointment.
"There's eight Champions League trophies that this team has won, and for me coming into this club, it's like that is the mark, this is the standard," Horan told Reuters from the team hotel in Prague.
The 29-year-old, who captains the United States national team, has won one of those eight titles with the club, and she puts Lyon's success down to the winning mentality they have fostered over the competition's 22-year history.
"Everything we did on the field was like, 'we're playing for each other. I'm trying to win this game with my teammates'," Horan said.
"I think it's players like Wendie (Renard), players like Ada (Hegerberg) that have instilled that and that have been here for such a long time, that's now our responsibility to keep carrying that."
A World Cup winner in 2019, Horan says the winning mentality in Lyon is similar to that in the U.S. national team.
"In the U.S. sense, we're a little psycho in that in that way - I mean, we will do anything, anything in our power (to win)," she explained.
GRITTY AND INTENSE
"That could be not playing well and just gutting it out, that gritty, intense game where you're like, no matter what, I know we're winning this game, but it just might not be pretty.
"I think here at Lyon, I feel like we find a way to win or find a way to do something, but still have that sense of football and that sense of 'we want to do it in this way'.”
Horan beams with pride about her achievements in Europe, but bristles at the suggestion that Lyon have been caught up and perhaps overtaken in recent years by the likes of reigning champions Barcelona.
"I think it's unfortunate people don't think of us at the top of the pile, because we are such an incredible team. You look at the players that are on our team and I always look at us that we are at the top," she said.
"We want to play against the best version of Barca, the best version of Chelsea, the best version of all these teams, that makes it much greater, and obviously greater for the spectator."
Growing up in Colorado, Horan was obsessed with the men's Champions League and she hopes that the women's competition will attract many more viewers around the world this season.
"It annoys me that it (the women's competition) is not talked about more. When I was younger, all I was watching was men's, I couldn't watch the women's Champions League – like, I couldn't find anywhere," she added.
"It wasn't a thing, I barely even knew about it, so I really, really hope that we get more viewership, that people are more in the know."
If all goes according to plan this Champions League campaign will end with a ninth victory in the final for Lyon in Bilbao next May, but first they have to get past Slavia Prague, Brann of Norway and Austrian side St. Poelten in the group stage.
"I think every team will make try to make it as difficult as possible for us, but it's our job to take that level up a notch, and I think it's going to be super exciting," Horan said.
