Chelsea are currently in 15th place this season and having suffered three defeats in a week, pressure on Mourinho's role at the club has been building.
However, Lampard, who won the Premier League twice whilst under Mourinho in 2004/05 and 2005/06, has urged that the club allow the Portuguese manager more time to turn the results around.
Lampard was speaking to Sky Sports and did admit that the results need to change quickly.
Lampard said: "I think they should stick with him but results certainly need to change now.
"Chelsea is a unique club. We all know the structure of the club and there's such a desire to win and a pressure. The owner, the board, the directors have taken decisions to win.
"What has been said over the past two or three years the club wants stability and a longer game.
"How important is stability? If you're getting results I suppose you're not that concerned. Manchester United was the ideal with Sir Alex Ferguson being there, the great Liverpool managers of the past again was the perfect ideal.
"I think it makes sense, you want to see a manager staying and a club successful. You want to see young players coming through to the team."
"That's the intriguing thing at the moment to see if they stick with [Mourinho]. He has got the best record Chelsea have had as a manager, he's a proven world class manager."