The Blues will bid to avoid surrendering an unprecedented fifth trophy before Christmas when they take on the Whites in Wednesday's Capital One Cup quarter-final at Elland Road.
They returned to London on Monday following yet another major disappointment this season after suffering a Club World Cup final defeat against Corinthians at the weekend.
And Leeds would love nothing more than to pile on the misery for Rafael Benitez's men.
Lampard is the only fit member of the current Chelsea squad with prior experience of what is one of the most acrimonious fixtures in English football and he has wasted no time filling them in on what to expect.
Spain winger Mata, who moved to Stamford Bridge at the start of last season, said: "Lampard told me about the rivalry. He told me the Seventies was when it started.
"They are always difficult games, competitive between supporters. We just want to play and, if it is possible, to win."
Chelsea must somehow lift themselves physically and mentally from their arduous trip to Japan for what is bound to be another war of attrition.
Lampard warned they face being dumped out of another competition if they fail to show power and passion at Elland Road.
The midfielder said: "There's a rivalry, we're aware of it and we have to play on the pitch with passion and do the physical side of things up there, because they're going to be right at it.
"We can't expect to go up there and tap it around and get a result. We have to do both sides."
Having let four pieces of silverware slip through their fingers already this season, Chelsea's young guns are in danger of becoming a generation of also-rans.
Lampard, who returned to captain the side on Sunday following what has been an injury-hit 2012, is a proven winner and bristled at suggestions more recent recruits did not possess the same mentality.
The midfielder, who declared himself fit enough to start again at Elland Road, said: "You can't go and win every tournament every year.
"We've never done that. No-one does it.
"We've changed the personnel a bit this year and there's been a bedding-in process and we've changed the manager, so there's been quite a few circumstances this year.
"We just have to try to improve and play better, simple as that."