The Russian took control of the Stamford Bridge side back in 2003 and since then they have won three Premier League titles, three FA Cups and two League Cups.
But the Champions League continues to elude Chelsea who must overcome a 1-0 first leg defeat when they travel to Old Trafford to face Manchester United.
Eyes on the prize: Frank Lampard (centre) trains with his teammates ahead of the clash with United
'Everything I've achieved in the last 10 years has only been possible because of the owner's investment,' Lampard told The Sun.
'I never envisaged that we would be winning league titles, competing in the Champions League and fighting on all fronts year after year so quickly.
'Everything changed when Mr Abramovich arrived in 2003. He has made a huge investment and we are all very thankful.
'I'd be very proud to win the Champions League for a lot of reasons but I definitely understand the thought process that we owe it to him towin it.
'He never sits us down and says "You must win the Champions League, this is the main thing". But we all know it would be a fantastic thing to him.
'And he deserves it for all that he has given to the club.'
Gutted: Chelsea lost the 2008 Champions League final to United
But Lampard knows Chelsea will need to find another gear if they are to progress to the semi-finals after United won at Stamford Bridge for the first time since 2002 last week.
Former Chelsea assistant boss Ray Wilkins described the Blues' efforts as 'gutless' and Lampard insisted: 'I have no problem with Ray saying that.
'I wouldn't necessarily agree we were gutless but we definitely lacked the edge you would expect us to have in the quarter-finals of the Champions League.
'That is something to address at Old Trafford if we're going to inject something into our game we didn't have the other night.
Lampard has endured a frustrating season having missed more than three months of action due to a persistent groin injury.
By the time he returned to action in mid-December, Chelsea were in the middle of a desperate run of form which left their hopes of retaining the Premier League title in tatters.
Body blow: Chelsea trail United thanks to Wayne Rooney's first leg strike
Now the Champions League is their last realistic hope of success - and Lampard admits the prospect of playing out the rest of the season with nothing to play for is a strange one.
He admitted: 'We started the season so well that no one saw what was coming next.
'We hit a brick wall and maybe we stopped doing the things which have made us so successful in the past.
'Whether that was down to over-confidence or whether we slacked off in training, it's hard to tell.
'I don't buy excuses, the whole Ray Wilkins leaving thing and stuff like that.
'Those things are not an excuse for the players. It's down to us as individuals to carry on doing the right things.
Breaking up is hard to do: Chelsea seemed to suffer when Ray Wilkins (right) left
'From winning games comfortably every week, we suddenly went to wondering where our next win was coming from. Every team has a dip but ours was too prolonged considering the quality of the players we have in our squad.
'As the manager says, we went to sleep for two months and now we've woken up and we're trying to make it another successful season.
'If that doesn't happen, we know we're going to get criticised because people have high expectations of Chelsea - and that's only right.
'We've been very lucky to have challenged right to the end of the season for the past six years.'"But we have to realise that everything won't always go our way so this game at Old Trafford is huge.
'The Champions League is a competition we've never won despite all our other successes.
'But this year it's even more important because we're not in our usual position of being out in front in the league.
'So now we have to perform at our best and take faith from the way we've won at Old Trafford before.
'If we do that, we're very capable of going through to the semi-finals.'
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