But the Brazilian has warned the team cannot afford to let momentum slip to turn around their poor start to the season.
The Reds finally pulled themselves out of the relegation zone on Sunday as they beat Bolton 1-0 at the Reebok Stadium with a late Maxi Rodriguez goal.
Coming after last week's victory over Blackburn, the result lifted them six places to 12th overnight but Lucas wants to press on.
The Brazilian said: "It's three points and I think everyone can see we are improving all the time.
"Of course we were under pressure. We still have to improve in the league but I think we are going the right way.
"In every game we are playing better and hopefully now in the next few games we get points and improve our position.
"The only way is playing well and I think winning will give everyone the confidence to keep going."
Lucas was impressed by the efforts of fellow South American Rodriguez, who is starting to establish himself as a fixture in the side.
The Argentinian was quiet early on at Bolton but grew into the game in the second half and went close with an overhead kick before settling the contest four minutes from time.
Rodriguez raced through to poke home the vital goal - his first strike since April - from a clever backheel by Fernando Torres and Lucas thought there was a touch of Brazilian magic about the move.
"I think Maxi scored a goal like Romario used to score, it was very similar," said the 23-year-old. "I was telling him it was a nice goal.
"I think Maxi is a very intelligent player. He is not so big, so has to play in space and cannot fight too much.
"He has a lot of technique so I think these kind of players always help you in the team.
"In the last two victories I think as a team everyone was playing really well and the understanding between the players everyone can see is better.
"I think these two victories will give us a lot of confidence to keep going."
Bolton made life difficult for Roy Hodgson's men and were unfortunate to see their unbeaten home record ended.
Both sides had their fair share of chances in an evenly-contested match and a draw, which would have been Bolton's seventh of the season, looked likely until Rodriguez's late intervention.
Lucas said: "It was a difficult game, of course. They have two big strikers and long balls always make it difficult for us.
"But at the end I think we tried to keep the ball on the ground and play our football, and at the end we could score a goal."
Such is the congested nature of the Premier League table that Bolton and Liverpool are now level on points.
That is a remarkable position given that a fortnight ago Liverpool were wallowing in their worst start to a season in 57 years while Bolton have been winning plaudits for their performances and results.
Much of that is down to manager Owen Coyle, who took over from Gary Megson in January.
Coyle feels his team still have much to be proud of and is confident they will soon rediscover their poise.
"Of course there are positives but I am disappointed to lose any game," Coyle said.
"Considering the effort the lads put in they didn't deserve that cruel ending.
"But that is the nature of football at this level.
"There is only one thing you do - you pick yourselves up, you come back in and work your socks off. You look to try to win the next game.
"It is obviously hurtful but it has happened. We can't affect it now, as much as we are disappointed.
"We will go back into work, look to get a smile on our face and go and work hard again."