Don't know. This would require knowledge of 18th-century lotteries in some country - France, Italy? - and some knowledge of the life of the person who got a lottery position and who wrote about music. It could be a job as director of the national lottery. It could be a job as court musician awared by lottery. We need the context: the source of your sentence, who wrote it, and who it's about and where.
"He" is http://en.wikipedia.org/wiki/Friedrich_Wilhelm_Marpurg
"This topic" is music. In 1760, he received an appointment to the Royal Prussian Lotteries, whose director he became in 1763, receiving the title of War Councillor. ...
Marpurg published the bulk of his writings on music between 1750 and 1763. After he had attained his lottery position in 1763, he penned two works on this topic but continued to write on wider areas of music.
So "his lottery position" is simply his job working as director for the lottery.
Edit: Actually, I think "this topic" must be something to do with his lottery work, since it seems to be set in contrast to his previous and subsequent writing on music.