Palace bypassed AEK Larnaca in the round of 16 in Cyprus on Thursday, winning 2-1 in the second leg after a goalless first leg at Selhurst Park.
With Palace only two ties from May’s showpiece in Leipzig, Oliver Glasner’s outfit will face six-time European finalists Fiorentina in the last eight.
Despite the pedigree of opposition ramping up, Palace defender Lacroix is determined to add the Conference League to Palace’s trophy cabinet to glimmer alongside the FA Cup and Community Shield.
“We did a lot to be in this competition, and we don't want to just say: ‘Okay, we are here just to play’. No. We want to win this cup,” Lacroix told the News Shopper.
“We are proud of what we’ve done, but this is not enough. You always want more. This is why the competition is not finished.
“We now have another two games to play and we will do everything to go until the end because this is the goal.
“We don't want to say: ‘We got to the quarter-final or the semi-final or the final’. No, we want to do something in this competition.
“It's always lovely to make history, especially for a club like this. We want to write this story. It's not finished.
“Like the gaffer says: ‘We don't have a ceiling’. We want to go further, and we want to create another legend.”
Lacroix led the celebrations in Larnaca, revving up the 700 travelling fans before they frantically booked flights to Florence for the next round.
Even on an empty tank after 120 minutes of football, the 25-year-old could not resist his signature fist pump celebration.
His teammates replicated the celebration in a united line shortly after, somewhat reminiscent of scenes at Upton Park 12 years ago when Palace secured back-to-back Premier League seasons.
“I want to give my last power, my last energy to them. When you finish the game, you're tired, you’ve given everything, but you still have something for them to say: ‘We fight until the very, very end. We won. We are together’.
“To say thank you, to celebrate together, it's a beautiful image when all of the team did the celebration with us.”
Despite not being named in the French squad for the final round of fixtures before the World Cup squads are announced, Lacroix is still dreaming of a place on the plane, having represented France from Under-16s to Under-20s.
“This is in my mind. I want to play for my nation. We have a beautiful squad. The World Cup in the USA is a beautiful competition.
“It would be a big achievement. I’m proud of where I come from, and the work I've done with all the people around me.
“Not only my achievement, but this would be the achievement of my family, the people around me who helped me. My dream is to win the World Cup.”