Luiz, 32, made a deadline day move across London to Arsenal where he signed a two-year contract after spending three seasons in a second stint with Chelsea. He made his Arsenal debut last weekend in a 2-1 home win over Burnley.
With Chelsea operating under a FIFA transfer ban, Lampard's policy has been to build the side with younger players, choosing to start Andreas Christensen and Kurt Zouma in central defence in his first two league games.
"Everyone knows I was so happy in Chelsea and won many trophies there. I had a real honest conversation with Lamps and Lamps had different ideas for his plans for the year," Luiz told reporters.
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"So the best way for me to respect the club where I can was to move on, try a new challenge and give him the opportunity to do his job.
"I'm so happy here as since the first day I felt welcome. This is a big club and I want to be here and see it shine on the pitch and outside."
Luiz said he could have remained at Stamford Bridge, where he had signed a new two-year contract extension at the end of last season after helping the club finish third in the league, but chose to seek a new challenge.
"I am a guy with ambition and that is why I moved," Luiz added. "I could have chosen a comfortable zone and got money and be cool and that is it.
"But I like a new a challenge and new things in my life."