Blue + Chocolate = MauveI don’t really understand the chocolate/mauve coloration.
Both genes are a dilute of Black but act independently so a bird could be Blue, Splash, Chocolate, Mauve or Splash Mauve depending on the number of genes inherited. A Mauve Splash would have two copies of the Blue gene in addition to the Chocolate.
Crossing Lavender into BBS and Chocolate =

But if you insist on doing it, as the Mauve Splash hen carries no Lavender gene treat the male as Black. All the offspring will be split to Lavender though so breeding them to one another or him over his daughters could yield Lavender again.
Chocolate is sex-linked, so I believe you should be able to get Chocolate from a Lavender x Mauve Splash breeding; however, it would be female? I think. There's a reason I don't like working with Mauve despite having it. lol
We'll see what nicalandia says.