Midfield star Lampard revealed he was "desperate" for the Blues' goalscoring "machine" to sign a new contract, with Drogba currently looking destined to quit Stamford Bridge at the end of the season.
Lampard acknowledged it would be impossible for Chelsea to fill the void left by a man who on Saturday became the first player to score in four FA Cup finals and who has netted in all eight cup ties he has played at Wembley.
"He's unique," Lampard said after setting up another goal for Drogba in the 2-1 win over Liverpool.
"There is no-one like Didier as a player, not with the kind of bulldozer kind of thing he has got and with the sublime touch and finish that he has got.
"Everyone has to move on at some stage and you have to find a different player or different way of playing but for what he has done at this club, he deserves everything."
Drogba, 34, snubbed Chelsea's offer of a one-year contract extension, while they in turn refused to bow to his demands for a two-year deal.
Lampard added: "I'm desperate for him to stay. He is a magnificent player. He's a machine.
"His body is a machine, when you look at him stripped down. He's lost no pace, he's lost none of his finishing instinct.
"As a man, I love Didier and whatever he decides to do, whether he stays or whatever, he has been a hero for this club and will go down as a legend."
Opposition defenders would be delighted to see the back of Drogba, who has been linked with lucrative moves to China, the Middle East, France, the United States.
"He's such a handful," Lampard said.
"It's been a pleasure to play with him and it would be a pleasure to carry on playing with him because he gives defenders such a hard time.
"He is not just that big man. He scores goals that matter and that's priceless."
Drogba is not the only player Chelsea will struggle to replace in the coming years, with Lampard himself and John Terry also the wrong side of 30 and Petr Cech fast approaching that landmark.
Cech proved he was as good as ever by producing one of the greatest saves in FA Cup final history to turn Andy Carroll's bullet header onto the crossbar and seal the Blues' win.
Lampard, 33, said: "I was calling him Gordon Banks in the dressing room because, from where I was - and I didn't get a great view of it - it was a goal, simple as that, once it was set up for Andy Carroll.
"Petr won that game for us with that save alone."
Saturday's victory handed Lampard his ninth major trophy and he can reach double figures on May 19 with the biggest of the lot, the Champions League.
He said: "Four FA cups, three leagues, two Carling Cups. That's nine, isn't it? Ten would be nice!
Lampard admitted he could have never envisaged such a haul when he first joined Chelsea from West Ham 11 years ago.
"I knew it was a bigger club and huge step up with the support the size of the club," he said.
"But we have a lot to thank the owner for for that.
"We scraped into the Champions League the year before the owner came, but since he invested in the club, he's taken us different levels and I've been very fortunate to play amongst great squads since then.
"I didn't know it was going to be this good."
Beating Bayern Munich in their own back yard would top the lot and would also see Lampard lift the Champions League as captain, with suspended skipper John Terry alongside him.
Both have shared the honour of raising the club's last three major trophies but Lampard said: "We are not getting ahead of ourselves.
"I don't care if all 11, 15, 20 in the squad have our hands on the cup."