The Lada is a Fiat built under license in Russia. For a real Soviet era car try a Zaparoszets. They look like a downsized Chevy Corvair.
I know what a lada is. I also know that it became a bit of a punchline in its later years of production. The last one, a white station wagon was produced in 2012. They were occasionally seen on the roads in my home town as they were sold in Canada as the Riva, and I grew up in a border town. The zaprozhets is quite possibly the 2nd worst car the communists made (after the trabant).
CC