Lambert, who has been out of work since leaving Wolverhampton Wanderers last year, was in the stands at Old Trafford this evening to witness his new team lose 3-0 to Manchester United.
After the match, Fletcher told Sky Sports News: "A new manager does give players a lift, it's a clean slate for everyone, the lads know that. We are fighting for our lives, we are in a relegation battle.
"I have played with Paul Lambert on my Scotland debut which makes me feel old, he has done good jobs in difficult circumstances in the Premier League. I think we have a very good manager."
Lambert's first game in charge will be Saturday's home match against Huddersfield Town.