Nine-time winners Real have lost on their last three visits to the Stade Gerland, including last season when they crashed out at the first knockout round stage for the sixth season in a row.
"They are different compared to last year. They are perhaps a bit more balanced... especially in midfield," Lyon coach Claude Puel told a news conference almost entirely dominated by questions about Real rather than his team.
"Mourinho is part of that."
Mourinho lifted the European Cup with Porto in 2004 and repeated the triumph with Inter Milan last season before heading to Real to try to become the first coach to win the trophy with three clubs.
Winger Angel Di Maria has also joined Real this term along with Germans Mesut Ozil and Sami Khedira, so Lyon centre back Cris is not reading too much into the French side's recent jinx over the Spaniards.
"Lots has changed, new players on each side, a new coach on their side. What happened has happened but this is a new story," the Brazilian said before Tuesday's encounter in the industrial and gastronomic heart of France.
Cris could also come face former Lyon striker Karim Benzema if the hit-and-miss Frenchman gets the nod ahead of Emmanuel Adebayor to start for Real.
"At Lyon he didn't have much competition. Real is a big club and there is competition for places and he has had to adapt," the defender added.
"Now he is doing well, he played well in the recent France v Brazil game and he's got a bit more confidence. He's an important player, a striker."
Lyon have come into form domestically at the perfect time, scoring four goals in each of their last two wins over St Etienne in the derby and against AS Nancy on Friday.
But relaxed coach Puel, who spent half the news conference giggling, is unsure how much his side's newfound confidence will help on Tuesday.
"It's another match, against another team," he said.
