The Brazil international departed the Blues on deadline day after a whirlwind 48-hour period which saw reports emerge of a major disagreement.
Despite being unable to sign a replacement due to a transfer ban, Lampard made the decision to let Luiz go to the Gunners.
Unai Emery was happy to snap him up for a bargain £8m after losing club captain Laurent Koscielny and was keen to acquire some experience.
And Luiz has opened up on the bust-up between him and Lampard that led to his surprising exit.
He told Brazilian journalist Mauro Cezar: “I always liked Chelsea, no doubt.
“A new moment has come in my career, a new cycle where I have had the opportunity to move to another major club, pursuing ambitions to win titles.
“I saw a possibility of writing a new story in a new place, but I am forever grateful to Chelsea, to all people, to friendships that are for life.
“I get messages to this day from everyone at the club because what I had there was true.”
When pressed on what made him leave, Luiz added: “It was an individual decision made through honest conversation – between me and Frank Lampard , no one else.
“We had a different idea of the future of the game and that’s why I chose to take a new path.
“It’s always very difficult because of the rivalry, but I made the decision to leave Chelsea even before receiving Arsenal’s bid.
“As soon as I decided to leave Chelsea – after a few days – Arsenal’s proposal came, and as it was another great club, I didn’t think twice.
“It’s hard for rivalry, yes, but I couldn’t help but live a new story, in a new place, in a big club just because of the rivalry.”