Abramovich famously fell in love with Europe's premier club competition when he watched Manchester United play Real Madrid in a thrilling tie eight years ago.
And since buying Chelsea later that same year, the Russian billionaire has become obsessed with winning the European Cup.
Never again: Frank Lampard is determined to overcome Chelsea's 2008 Champions League final heart ache
No team has gone closer in the interim without actually achieving that dream and Abramovich has been painted as a character who has become increasingly impatient with the failure of successive managers to deliver the ultimate prize.
But ahead of tonight's quarter-final first leg against Manchester United - a repeat of the 2008 final - Blues midfielder Lampard claimed the club's owner knew full well the enormity of the challenge.
'I'm sure the owner would be very pleased for us to win it,' Lampard said.
'But at the same time, he doesn't come in every day and knock our door down, saying,
'Why have I not won this yet?'
'He understands it's the most difficult competition in football.'
Roman's right: Lampard believes it is more than acceptable for Chelsea owner Abramovich to demand success
Lampard, who has helped Chelsea deliver Abramovich every major domestic trophy since the Russian's arrival, added: "I think we've given him some very good times and I know the owner has appreciated it from how he's enjoyed them with us when we've won titles and with the cups.
'But the Champions League's a huge thing. You want to be known as the best team in Europe by having that trophy.'
Lampard has also come to accept Chelsea do not have a God-given right to win the Champions League, something forged by four-semi final defeats as well as the agony of the final three years ago.
'When you play for a long period of time, as I have here, you see the ups and downs - you collect them,' said the England star, who insisted revenge for Moscow would be the furthest thing from his mind this evening.
'You don't any feel thoughts of revenge or anything against anyone. You understand you can't always be successful and win.'
Happy days: England midfielder Lampard is set to make a landmark 500th appearance for Chelsea
Lampard has had almost a decade of highs and lows at Stamford Bridge and reaches a personal milestone tonight when he makes his 500th Chelsea appearance.
He will become only the fourth man to achieve that feat after club legends Ron Harris, Peter Bonetti and John Hollins.
'It's very humbling - a group I didn't think I'd get into when I came here 10 years ago,' Lampard said.
'They're the big names people that talk about from years gone by.'
He added: 'I'm not thinking of the end. Thirty-two now is not what it was 10 years ago.
'Hopefully I can perform well into my thirties. The Giggses, Maldinis, Scholeses have all gone on and played well into their later 30s. I would love to be able to do that.'
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Explore more:People: Roman Abramovich, Frank Lampard, John Hollins Places: Moscow, United Kingdom, Europe