Lehmann, signed from Borussia Dortmund last week for £1million, was rarely tested in the first half and played no part after the break with Stuart Taylor taking over in goal.
Wenger has challenged 22-yearold Taylor to push Lehmann hard and fight to be the successor to David Seaman.
Taylor - close to agreeing a two-year extension to his contract - said: "The manager said to me he needed to sign another goalkeeper. But he did say, 'If you are playing well, I will play you. It is up to you to push for a place.'
"It was nice to hear that and I know it is up to me to work hard and to play as well as I can. It helps to have a goalkeeper of his ability around. With David Seaman, I was able to learn things and hopefully I can also learn from Jens. He is a player of quality and experience.
"I think the manager is a man of his word. If I am doing well and if Jens is going through a rough patch, then hopefully I will get my chance. But it up to me. I have to make sure that I am playing well.
"I am still only 22 and have a lot of time left. If I can play a few games like I did last season and the season before and I play well, then I will be happy.
"Jens has only been with us a very short time [he joined up on Sunday and left at half-time last night to catch a plane back to Germany] but he seems a nice bloke.
"He speaks fluent English, which is a help. Sometimes when foreign players come to the club and they don't know the language, it is hard to communicate. It makes it a lot easier when people can speak English. I am looking forward to working with him."
Wenger believes his pre-season preparations - in which Taylor has figured prominently - have progressed exactly to plan. "The physical work is behind us and now we have a phase of real competition against Celtic, Rangers and Manchester United. They will be really competitive games.
"Robert Pires, Thierry Henry and Sylvain Wiltord should be ready for Manchester United [in the Community Shield].
"Pre-season has also given me the chance to try players in different positions and to see the progress of the young players. Kolo Toure looked good in central defence against Besiktas and Jermaine Pennant has been doing well. And Dennis Bergkamp looks sharp and motivated."
