Two goals from defender Branislav Ivanovic and a third from Didier Drogba gave Chelsea an emphatic victory, after Liverpool's Fernando Torres had put the Reds in front in the sixth minute.
Chelsea are favourites to reach the semi-finals of the competition, and Lampard was buoyed by the performance and result - amid speculation that Carlo Ancelotti is to join the Blues as coach in June.
Latest media reports suggest the AC Milan coach has accepted a £5.8million deal to replace interim coach Guus Hiddink, but Chelsea have officially dismissed them as "just speculation".
Ancelotti has long been favourite to become the next Chelsea coach, but the clamour for Hiddink to stay is expected to grow following the performance against Liverpool.
Hiddink has made it clear he will return to manage the Russia national side at the end of the campaign. But helping Chelsea to glory in the Barclays Premier League, the Champions League and the FA Cup may go some way to changing his mind.
Midfielder Lampard was at his influential best against Liverpool, who will go to Stamford Bridge next Tuesday requiring at least three goals to have any chance of turning the tie in their favour.
Lampard is not ready, though, to focus solely on winning the Champions League this season.
"This result sets the tone really," he said.
"Who knows what can happen in the league and the FA Cup?
"Everything is still up for grabs, even though we are behind in the league. It is important that we keep to the standard we played against Liverpool. When we look at the strength of our team throughout the pitch, we are as good as anybody.
"There have been times this season when we have not performed at our best - and we have to take responsibility for that as individuals and as a team. But it is done and in the past.
"All we can affect is what we are going to do in the future. There have been times when we've been below par this season. But when we play like we did against Liverpool, then we can get such results.
"We hope if we can carry on playing like that we will put fear into a lot of teams. But we must keep to those high standards.
"We are points behind in the league - so we know the situation, and all we can do is worry about ourselves and keep winning games.
"We need to set the standard we have shown against Liverpool. It gives us confidence. But we cannot relax, and there is everything to play for. We have to try and keep on top form in every game."
Chelsea's advantage should make the return leg at home a mere formality, but the ever-cautious Lampard is taking nothing for granted.
"We were disappointed we didn't score more, especially towards the end of the game when they opened up and we had two or three chances to make it four or five," he added.
"That would have put the game out of sight. At the moment, it is not out of sight. Liverpool are a strong team - they beat Manchester United 4-1 - and we have to be on our game next week and make sure we don't slip up.
"But it is a fantastic first result. We were very organised, played good football and were very dangerous on the break. We changed ourselves tactically a little bit, and they found it hard to deal with."
One low point for Chelsea was captain John Terry's booking for a challenge on goalkeeper Jose Reina. Terry is now suspended for the return leg, but Lampard believes they have enough in reserve to deal with his absence - and he also criticised Liverpool's players for urging the referee to show the defender a yellow card.
"We hope we'll have enough in the squad," he said.
"Ricardo Carvalho looks as though he will be fit - and if we can go through then John will be on a clean bill going into the semi-final. It was unfortunate that the Liverpool players ran round to make sure he did get booked."