I'm having a similar problem to this thread, but I am not using Google Fonts. Rather, I downloaded the fonts from the Lato website (specifically version 2.015) and installed them onto my machine (Windows 10). Yet InDesign still says that I am missing many Lato fonts:
But they're definitely on my computer:
The only thing I can think of is that maybe I didn't install the OTF versions (they had .ttf file extensions). But I don't understand why that would make a difference. Indeed, the notes for Lato version 1.105 states that others have had this problem and therefore they included an OTF subfolder (which wasn't in version 2.015). I am also contacting the Lato devs, because I assume that much of these questions are things that only they can answer, but I wanted to see if anyone else has had this problem with InDesign before.