could not load kernel32.dll, status c0000135
On my Debian Trixie system, kernel32.dll is in the libwine package:
$ apt-file search kernel32.dll
libwine: /usr/lib/x86_64-linux-gnu/wine/x86_64-windows/kernel32.dll
$ apt-file search -a i386 kernel32.dll
libwine: /usr/lib/i386-linux-gnu/wine/i386-windows/kernel32.dll
$
I have no idea what Linux distribution you're using, but if it's Debian-family, maybe:
$ sudo apt install libwine:amd64 libwine:i386
That'll get both the 32-bit and 64-bit WINE libraries.
It sounds like Battle.net is a 32-bit Windows binary, whereas World of Warcraft itself is a 64-bit binary. I assume that the Battle.net binary might also be a 32-bit binary, and it looks like you're running a 64-bit WINE binary (see the x86_64 thing in the above path that Lutris is running). Maybe you only have the 64-bit WINE libraries installed, and it can't run the 32-bit Battle.net installer? I'm guessing, mind.
I don't use Lutris, so can't provide any advice there.