Do you know Tony Griffiths' Web-Site: http://www.lathes.co.uk/andra/
I think is pretty much sums up the story. The company was located in Limbach-Oberfrohna, near Chemnitz (or Karl-Marx-Stadt, as it was called during GDR-times).
In this little town several 'People's Factories' ('Volkseigene Betriebe', VEB) specialising in precision machinery were located. Saupe, who made small lathes, was one of them. Some of them were nationalised small private firms that continued to operate like small firms, often with their previous owners as managing directors. The scroll-chuck manufacturer Koch (http://kochmaschinenbau.de/en/products/precision-clamping-chucks/watchmaker-lever-scroll-chuck/
) was/is one them. They made chucks for AndrÃ¤&Zwingenberger, Saupe, and others.
I can't comment authoritatively on the colours of the lathes, but would assume that black models are early ones, following the pre-war practice of painting small precision machines. Later, shapes became more angular and they seem to have switched to a light green (reseda green), which was the standard machine-tools colour in Germany, West and East. In more recent years they had a 'hammerite' finish I believe (of which personally I am not so fond of ...).
Georg Jacob GmbH, who are mentioned in above article on the AndrÃ¤&Zwingenberger lathes, were a major watchmakers' and jewellers' supply house from the early years of the 20th century on and located in Leipzig. They published elaborate catalogues in book form that today fetch high prices - I have the sought-after 1911 edition