Hmmm... The
wiki article links to
here, which discusses the L4 and L5 regions of the moon's orbit. It seems every body in the solar system has it's own set of Lagrange points labeled similarly, including the moons. The wording of the wiki article also threw me off, as it says, "...which is stable and stationary relative to both the Earth and Moon facilitating simple travel and communications." The mention of both the Earth and the Moon made me assume it meant the Lagrange points belonging to the Moon's orbit.
The wiki article should probably be edited to be more clear regarding this.
[edit]
I went ahead and edited the wiki article.
Also, moving the spinner to the Earth-Sun L5 region would mean the cylinder axis would always be aligned with the Sun, meaning constant sunlight through the glass dome at the end. Not sure if that's a good or bad thing...