The LAFCA is a big award ceremony, one of the 4 to 5 big ones prior to the Academy Awards. I believe it is more critical than even the Oscars even. So there is no doubt that this is a big win.
I doubt Your name. will win since a lot of Miyazaki films don’t win.
Your name. is one of the highest grossing anime- no Japanese films of all time. It was created by Makoto Shinkai, who once did a whole anime nearly by himself, which is feat normally for hundred man crews if smallest.
It did not take Best Foreign film however as it went to Oldboy director Park Chan-Wook’s The Handmaiden. The Handmaiden also took Best Production Design.