The 30-year-old Brazilian, who played 346 times in his 10 years at Liverpool, after joining from Gremio in 2007, signed for the Serie A club after passing a medical in Rome.
British media reports said Liverpool had accepted a bid of five million pounds ($6.52 million) for Lucas, who has 24 caps.
In an open letter to the Premier League club's fans, he said the only reason he had left was "to play as much as I possibly can".
"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," he said in the letter published on the club's website (www.liverpoolfc.com).
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"But that would go against everything that I believe in as a footballer and as a competitor."
Lucas, who had been Liverpool's longest-serving current player, said: "Liverpool as a club and Liverpool as a city is a unique place. I think it's different from everywhere."
Lazio finished fifth in Serie A in 2016/17.
($1 = 0.7665 pounds)
(Reporting by Neville Dalton; Editing by Christian Radnedge)
