Well, he had a cousin who made them. I like to imagine that they were
pity purchases, but he was more likely acting as an agent.
For the lute-harpsichords of Johann Nicolaus Bach (1669-1753) we rely on the Musica organica organoedi (Berlin, 1768) of Jakob Adlung (1699-1762), but there is no evidence that his second cousin, JSB, owned any of the kinds that he (JNB) made.
With Zacharias Hildebrand we are on surer ground. An editorial note by Johann Friedrich Agricola (JSB’s pupil) in Adlung (p. 139) tells us that:
“The author of these notes remembers having seen at Leipzig in about 1740 [when a pupil] a lautenclavicymbel designed by Herr Johann Sebastian Bach and made by [his preferred organbuilder] Zacharias Hildebrand.” The description which follows is in some respects the most detailed we have.
Of course, Adlung does not say that the example he had seen actually belonged to JSB or that it was in his house when he died, but he does unequivocally associate the instrument with the composer, casting him in the expert role of designer. However, read in the light of the 1750 specificatio, with Occam’s razor in hand, it is likely that JSB designed the instrument not for the good burgers of Leipzig but with his own preeminent musical use there in mind.