The 6in (15cm) drawing shows "the Old Handball Court, Nelson, Glamorgan", now a listed building in Caerphilly county.
Peter Wilson fine art auctioneers said Lowry was introduced to the south Wales Valleys by Ebbw Vale businessman Monty Bloom.
Signed and dated 6 November 1961, it is thought to have been sketched by Lowry as he sat in a nearby cafe.
"Bloom recognised the appeal the grim contrast of spoil hills side by side with real mountains would have on the artist," Peter Wilson auctioneers said.
"Aged 77, Lowry embarked on a new era of painting inspired by the Welsh scenery and began working in a new, intuitive and experimental way.
"Together, Lowry and Bloom made visits to the area every six months or so and it is thought that this sketch may have been made upon his return from such a trip."
Lowry gave the napkin sketch to artist Percy Warburton, who would later pass it on to the family who put it up for auction on Thursday.
It was bought by a private collector from the Midlands.
A sketch on a napkin by the artist LS Lowry has been sold at auction for £9,000.