Not sure how much Luiz will directly improve the overall standard of our defending? Maybe a little, but probably not a great deal. My main hopes for his arrival are the indirect benefits...
1) It pushes Mustafi out of the side...
2) It might even push Xhaka out of the side (if Luiz can offer us that same range of passing, but from the back line, then what does Xhaka really add to the side?)...
3) If we can bench Xhaka more often, then we can start selecting more dynamic, more press-resistant CMs to play in front of the defence (Ceballos, Willock, Torreira, Douzi)...
All of which will hopefully mean less hospital passes being made and less forced errors being made in and around the defence.
(I'm also hoping we'll see some indirect defensive improvement from the changes in shape and system we can now work with, now we have wingers and a few defenders who can play in a back 4.)