Lamps ended up at City via NYFC anyway, he didn't directly join them and who knows what the story is behind the scenes but I believe they did have some sort of power over him + the appeal of playing at top level again.
I really want to have another playing join the Chelsea book of legends, maybe we're expecting a bit much of Luiz? Cech and others stayed and fought for their places despite losing playing time.
The best case scenario is if Luiz joins Arse, he writes a heartfelt farewell message and promptly costs them in performance, then rejoins Chelsea after retiring as a coach or rep in some way.