Lucas had spent the last 10 seasons at Anfield but after only being used on a rotational basis last season, it soon became clear that he would leave the Merseyside giants this summer.
It had initially been suggested that he would sign a deal with Brazilian side Gremio, but he has instead opted to link up with Serie A giants Lazio.
The 30-year-old told the English club's official 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."
Lucas made just 12 starts in the Premier League last season, although a further 12 appearances were made from the bench.