Lucas has thanked Liverpool’s “special” supporters after completing his permanent transfer to Lazio.
He told the Reds’ website: “Liverpool as a club and Liverpool as a city is a unique place. I think it’s different from everywhere.
“The fans are a big part of the club, probably the most important part of the club, and without them Liverpool wouldn’t be the same club I would say.
“Thank you for all the support, especially in difficult times, that’s when it means a lot. We all know that Liverpool fans are really special and they were always here for me.
“I’ll always be watching and supporting Liverpool and for sure I’ll be back, in the city to visit friends and watch games in the future.”
Lucas, who was entering the final year of his contract, maintains the club and the city will always hold a special place in his heart.
Liverpool added in a statement: “Everyone at Liverpool FC thanks Lucas for his immense contribution to the club and wishes him and his family all the best for the future.”
Following his departure, Lucas, who is a trustee of the LFC Foundation, published an open letter to Liverpool fans.
He said: “This is one of the greatest clubs in the world and my intention had always been to spend the rest of my career here, but the less I have been able to play, the more I have realised that I need to go to another club if I want to play as much as I possibly can.
“When you love a club and a city as much as I love Liverpool that isn’t an easy decision to come to. The easiest thing for me to do would be to stay here for as long as I can even if I do not expect to play so often, but that would go against everything that I believe in as a footballer and as a competitor.
“It is for that reason that I will be joining Lazio, which means my sadness at leaving Liverpool is accompanied by a real excitement that I will be representing one of Italy’s great clubs.”
Lucas added: “My family and myself will always be grateful for your support and for being part of this great club, which means we will also be sad now that the time has come for me to leave.
“All I can say now is that I hope more than anything else that the new season turns out to be a great one for my new club and my old club.”
In the last 18 months, Jurgen Klopp had asked Lucas to stay on to provide some much-needed experience, despite interest from a number of clubs in Turkey and Italy, but clearly decided not to stand in his way as he pursued regular first-team football elsewhere.
“I am not 100 percent sure, but I think for Lucas, [who’s had an] outstanding, fantastic time at Liverpool, we should talk about facts and not rumours. Maybe something, maybe not,” Klopp had said last week, before his squad travelled to Hong Kong to continue their preseason preparations.