Ziyech has transformed Chelsea's attack with two goals and three assists in his first five starts for the club and will be a key part of Lampard's plans to get the better of Jose Mourinho's Tottenham.
Lampard said, "It is very hard to fill one-for-one a player of Eden Hazard's talents. His input at the club was huge. To lose that you have to try to find a way around it with the transfer ban last year, it was more about the younger players coming in and how we could become more efficient as a team.
"I think we made really good steps on that front and now with the players we have brought in I would hate to give any of them the job or idea of 'you must replace Eden'. They have to focus on themselves.
"I remember Eden's first year or two at Chelsea. It was clear what an amazing player he was going to become but he also needed time to become that great player that we all now know and love as Chelsea people. The players we brought in all have potential in their own way to make the pathway to show how much they can give to the club but I certainly won't be throwing Eden Hazard comparisons at them. They have to do it in their own way."