Arsenal boss Arteta picked up his first piece of managerial silverware by seeing off Chelsea in the 2020 FA Cup final.
At the time, Lampard's star as a young manager was on the rise while Arteta was still battling to show he was the right man to address the slide in Arsenal's fortunes.
Now though, the tables have been turned and reports suggest Lampard is now in a battle to save his job.
But Arteta – who like Lampard captained the club he now manages – feels the former England international should be afforded more time to get things right at Stamford Bridge.
"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," said the Spaniard.
"He has huge experience as a player, he is an icon over there and 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."
In December, Arteta was the bookmakers' favourite to be the next Premier League managerial casualty.
A 3-1 home victory over Lampard's Chelsea on Boxing Day helped the Gunners get back on track and they have now won five of their last six games in all competitions.
Despite a rocky patch earlier in the season, the Arsenal hierarchy publicly backed Arteta – who believes managers are facing a difficult proposition with Covid protocols and a truncated season.
"I can only talk about what I have experienced," he replied when asked if he had empathy for Lampard's situation.
"What I have experienced, it was full support in difficult times. 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."