I have seen amateurs grinding lenses for telescopes entirely by hand using two glass disks and abrasive powders. No machine was required. Perhaps that technique was used 350 years ago as well?

I have never seen a lens grinding lathe, but I have noted that the word lathe is used for very different machines by people in different branches of mechanical work. I have seen a modern machine for grinding the concave side of eyeglass lenses, but I don't recall what it was called. It probably was a way of mechanizing the motions of the people I saw making lenses by hand. In some types of work, the name lathe is given to what a machinist would call a bench grinder or buffer.

A lathe of early design, but still recognizable to modern machinists as a lathe, would have been used to make the brass fittings for telescopes and microscopes. Such a lathe would have been about the same as those used for clock and watch work during the same period. In other words, you could study early horological tools, which might give you more information than restricting your search to optical tools.

Larry