The Reds moved to sixth on the table courtesy of Sunday's 3-2 victory over third-placed Tottenham and now sit seven points behind Chelsea in fourth and Lucas feels there could be some more improvement at Anfield.
"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."