The Reds currently sit seven points outside of the top four, and have a slim chance of earning a spot in Europe's elite competition following a 3-2 win over fellow challengers Tottenham Hotspur on Sunday.
The Brazilian has praised his side's current form and believes that they are hitting their peak at the right time.
"Our biggest virtue in this match was that we never stopped fighting. We didn't get upset at losing and showed our strength to come back," Lucas told Terra.
"We are improving at the right time and, because of that, we can dream of a Champions League place.
"It was our third consecutive victory, something that is worth a lot given the difficulty of the Premier League. We will continue to work hard, without fanfare, and things will come naturally."
Liverpool travel to Southampton on Saturday.