The England midfielder broke Tambling's record of 202 goals for Chelsea away to Aston Villa last week.
After agreeing a one-year contract extension, the 34-year-old is still hoping to add to his tally and revealed his pride in claiming a record that he believes might stand for some time to come.
"Unless we sign Lionel Messi in the next year or so, I think I have a chance of keeping it," he told The Sun.
"Especially If I can push it on a few more in the future. So, yes, it could last a while, especially considering the modern game.
"The old players stayed at clubs longer, had more associations with their clubs than they do now.
"But if in five to 10 years someone breaks it, then I hope I can pass it on with as much grace as Bobby has to me.
"Over the years I've got to know Bobby well and I am honoured to have been the one to match his record and break it.
"If it was from someone I didn't like, I might have rubbed his nose in it - but I am close with Bobby and his family.
"It's fantastic. No one can take away what we have done at the club. We are both part of the Chelsea family, the Chelsea history and I'm very, very proud."
Asked to pick his favourite, Lampard said: "Can we count the two I scored at Bolton to clinch the league in 2005 as just one? They were so important not just for me but the whole club.
"Then there was the goal against Barcelona where I turned and chipped it over Victor Valdes and into the top corner.
"And obviously my second at Villa last week because that was the one that clinched the record and was very special and emotional for me."