Despite the global nature of the Premier League, Lampard says local rivalry remains intense.
"Of course it does,' he told chelseafc.com.
"I think that rivalry between the fans is always there, in fact I think it grows almost every year and particularly with players who have been at their clubs long enough to understand the rivalry over the years, it stays as strong.
"Whether it is trying to beat Tottenham in the FA Cup semi-final, or finish above Arsenal and Tottenham in the league, it is always there and it is healthy.
"Everyone has different measures of success now,' he adds. 'Arsenal haven't won the league recently but they want to get into the top four every year. For us we are in that same boat with them and Spurs now but recently we have been all about winning the league.
"There is a rivalry between us but it has also turned into a battle about that third or fourth spot which has probably made it bigger this year."