Cole is hoping to feature against the USA in England's Group C opener on Saturday and believes Lampard will be unstoppable in the tournament if he finds the net in Rustenburg.
Lampard failed to score in the 2006 finals in Germany, despite playing every minute of his country's venture to the quarter-finals, and Cole says it is important his midfield colleagues share the burden of finding the net.
Cole said: "The best thing that would happen for England is for Frank to score in the first game. If he gets one he gets on a roll.
"He seems to score his goals in bunches and if we are going to do something in this tournament we are going to need Frankie to score two, three or four goals.
"We are also going to need Wazza (Wayne Rooney) to score four or five and ones and twos chipped in from everyone else because we are going to need goals from the midfield."
Cole's involvement in the tournament had been in doubt after a frustrating season at Chelsea as his hopes were hampered by a combination of injury and lack of game time.
The winger is fit and in contention to start after displaying a late burst of form in the Three Lions' pre-tournament training camp to make it into manager Fabio Capello's final squad.
But the former West Ham star said he was not content with just being involved in South Africa, revealing his desire to end England's barren run without major international silverware.
Cole, who is leaving Chelsea, added: "You might not play in a World Cup again and you don't like the idea of your lasting memory being a bad one. You want to finish well and look back on a good one.
"If it is the last one I play, we'll put everything in there to make sure it's as good as it can be. We all know the names of the 1966 winning team.
"There's been many a great English player that hasn't won a World Cup or a European Championship since then, and they'll still go down in history. But if you want to do the group thing, you have to win something."