It is a rare experience indeed to hear one!
My lute was built in Augsburg around 1590 by Sixtus Rauwolf and would originally have been probably a 7 or 8-course lute.
There is also inside the lute a label of Leonhard Mausiel of Nüremberg dated 1715 and undoubtedly this was the time when the lute was given its new neck and "updated" into an 11-course lute.
The 11-course lute was the most important type of lute during last half of the 17th century and the first quarter of the 18th century.
This "renaissance" lute therefore has been restored to its latest playable condition as an 11-course "baroque" lute, although it can also be strung as a 10-course lute in "renaissance" tuning.