I don't own it, but in the first view it looks like the Austrian one, isn't it?
That's an Austrian shop who tells us that the mug he sells is Austrian army issue. (Bundesheer)
army-warehouse.com
I think although Austria has a general conscription army there are compared to the US mug relatively few of these mugs. That's why I don't expect an aftermarket maker and I don't think that there is an issued one, as usual.
I am relatively well informed about what's offered at the market as I speak fluently German, French and English and spend quite a lot of time in bushcraft forums and on internet military surplus shop sites. And I spend my time with this hobby since decades and had a look in a lot of real surplus shops. I never have seen a lid for the Austrian mug.
There are a lot of videos at YouTube how to make such a lid from an aluminium plate.
I didn't do that myself but it looks pretty easy.