Lampard enjoyed a warm welcome at Chelsea due to his status as a club great, yet he is learning results must swiftly follow.
"I certainly found that it helps with knowing some faces behind the scenes, knowing the values, what the standards are and what the wants are," Lampard said.
"I think that can help probably in the early stages. I think after that, it probably levels out and your work is your work.
"No, [the honeymoon period] doesn't [last forever] and it shouldn't. But I'm sure fans will have a feeling for Arteta and want him to do well being one of their own."
Arteta is in his first head coaching position, but Lampard does not see his inexperience being a big factor given his work with Guardiola.
"He has worked under one of the greatest if not the greatest [managers] for a couple of years," said the Blues boss. "I think you don't know until you take the chance with somebody.
"Who's to say a manager is better or worse if they are in their first or 50th year of management?
"He was a very good player - intelligent, technical. He seemed to be a leader, not a fist-pumping kind but a leader in whatever teams he was playing in.
"I think the years he's had working with Guardiola put him in great stead. I don't think the question mark will be that.
"I think it will be purely on Arteta, the quality of him, and can he get Arsenal to the position they want to be in? Now it's his turn to make those decisions himself."