Lampard is under pressure at Stamford Bridge after a poor run of form that has left the Blues sitting eighth in the Premier League.
Chelsea have won just two of their last eight Premier League games and they now face a crucial run of matches against Wolves, Burnley and Tottenham.
Arteta, however, has come out and backed his fellow manager and urged Chelsea to give Lampard time to turn things around.
“I have known Frank for a few years and I spent some time with him and I would like the club to support him and give him a chance,” he said.
“He has huge experience as a player, he is an icon over there. He has done some really good things. You need time, and something we have not had in this calendar year is time to work on anything.”
Arteta was himself under pressure earlier this season after Arsenal’s form nosedived during November and December.
The Spaniard managed to turn things around – with, ironically, a win over Chelsea on Boxing Day kicking things off – and he has steadied the ship.
Arteta has thanked the Arsenal hierarchy for their support during that tough period, but admitted that is not always the case at other clubs.
“I can only talk about what I have experienced. What I have experienced, it was full support in difficult times,” said Arteta.
“The work you are doing behind the scenes, the methods you apply, the values you are trying to restore at the club, and the style you are trying to implement needs the support of results.
“Fortunately if they see what you are trying to do is going to have rewards in the future, and they are a little bit patient, most of the time it pays off. If everybody is convinced we are doing things the right way.
“I speak with a lot of managers and some of them have been in the game for over 30 years and they say they have never experienced something like that.
“This is a new game with new rules, there are so many things we cannot control. It is out of our hands in a lot of moments.
“So I listen a lot to that because we tend to put on more and more pressure and demands on ourselves, and it is a very strange league this season and you can see that.”