The Brazilian did admit there is an element of uncertainty surrounding some players' futures as well.
Klopp will take charge of his first Merseyside derby this evening, and after six months in charge of the Reds the German is now starting to find some sort of consistency as the Reds start to show their best form under him.
A win against Everton at Anfield tonight could take Liverpool up into sixth place in the league while they also have a Europa League semi-final to look forward to against Villarreal.
Lucas told Sky Sports: "We struggled to win games in a row, and we are now starting to do that. Defeats will always happen but we have a very relaxed place, and one where he shows he's believing in every single one of us. The proof is when he makes changes, the team still performs.
"We are on the right way to achieving good things."
There is an element of doubt about his future, as well as many others, with the following comment:
"Everyone wants to finish the season on a high, and in the future we never know. The manager will make his decision and we will have to wait to see who is in his plans.
"In football, things can change very quickly, good and bad, and you just have to live in the moment and do your best. The rest will take care of itself."
Lucas has been one player who has been linked with a move away from the club for the past couple of summers, but has ended up staying put, and experience is probably on his side when it comes to remaining at the club beyond this summer.
There have been suggestions that Klopp will look to make several changes during the summer as he seeks to build a side that can kick on next term.
Liverpool will be hoping the achievements start from this season with the opportunity to win the Europa League, and the reward of Champions League qualification that accompanies lifting the trophy in Basel next month, but a Merseyside derby victory to continue a good recent run is the immediate priority.