Lucas believes Liverpool will continue to improve over the course of the season as new players settle in and others are welcomed back from injury.
The Reds have made a solid start to the new campaign and are currently fifth in the Premier League after playing out a 1-1 draw with fierce rivals Manchester United at Anfield on Saturday.
Steven Gerrard returned to the starting XI against the Red Devils following a lengthy lay-off, while the likes of Glen Johnson and Daniel Agger are also pushing for recalls after getting back to fitness.
Competition for places has been increased by the arrival of several new faces over the summer, and Lucas has backed the Reds to mount a strong challenge this term.
"I think there is more to come," he told the Liverpool Echo.
"There are a lot of new players that came in over the summer and it always takes time to settle and build an understanding between the players."
Lucas will miss Saturday's clash with Norwich after picking up a fifth yellow card of the season, but he is confident Liverpool will return to winning ways after the draw against United.
"Unfortunately I will be out of the game because I am suspended, but I will be cheering the players on," he said.
"I think we deserved to win against Manchester United. We played really well and now we have to take the positives into the next game, hopefully get the three points and be closer to the top four.
"I think there is a lot to come and hopefully it will be a successful season for us.
"We are disappointed with the result because we wanted to win but you could see that we had a few players coming back from injury."