The Italian spent three years of his own playing career at the Stadio Olimpico with the Biancocelesti and believes it would be a good move for both Lampard and the Italian club.
"Lampard is a great player and a great professional, so I am certain he can play at least another two years at the top level," Di Matteo told Sky Sport Italia.
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The England midfielder has been linked with numerous Serie A clubs including AC Milan and Juventus, but has agreed terms on a move to LA Galaxy, as exclusively revealed by Goal.com.
Di Matteo was sacked from the Chelsea hot-seat earlier this season despite winning the club's only Champions League trophy just months prior to his dismissal, and says he was glad to hear fans chanting his name after his departure.
"It was an incredibly emotional experience and a very difficult achievement. I had three fantastic months on the Chelsea bench, but also tough, as we worked up to 18 hours a day to achieve our results," he added.
"I was pleased to hear the fans cheer my name after I left. It was love at first sight with the supporters the moment I arrived in London and I'm sure that love will continue over the years.
"Have I had any contact with Italian clubs? I prefer not to talk about this as I have a great deal of respect for the current coaches. In any case, I don't hide that I am very happy with what Lazio are doing in Serie A."