I’m familiar with the lettuce-tomato-onion being called a “California burger” as well, and I’m in Chicago. It’s not current nomenclature (which would, as you say, usually mean avocado on a burger or something of that nature), but I think there was a time California was strongly associated with fresh produce. (I guess it still is, but even moreso.) I know I’ve brought this up on the Dope before.
ETA: I could have sworn it was on this board, but I can’t find it. I checked another board and came up empty, except for a poster saying that growing up in Milwaukee, they called a burger with lettuce, tomato, and mayo or special sauce a “California Burger.”
ETA2: Here’s a thread from '04 where @chique reports a California Burger in central Minnessota being a burger with lettuce and tomato. It may well be an Upper Midwest/Great Lakes thing (oops, but you say you saw it in the PNW, so I guess it’s farther afield than that. I don’t think it’s particularly common anymore to refer to that as such):