snip
How fricking hard can it be to find a metric gear, given you have
others in the gear train and the original, though damaged one? Sheesh.
I'd *never* approach the lathe manufacturer in a case like this unless
the gear had internal splines or something really, really oddball. And
maybe not even then. You'd pay far more than a gear supplier would
charge.
PDW
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the problem may be that because metric gears are generally
specified by module and pd, it is difficult to identify. Try
this:

(1) Count the number of teeth on the good gear. (I sugest marking
a space and not the tooth where you start.)

(2) Measure the outside diameter of the good gear in m/m

(3) Add 2 to the number of teeth [step 1]

(4) Divide the outside diameter of the gear by the number of
teeth + 2. This will be the metric module, typically 1.00 or
1.50 for lathes in that size range.

(5) Measure the width of the teeth of the good gear in m/m.

Use google to look for gears you can adapt. If the gear cluster
is not hard you should be able to machine off the damaged gear,
and modify an existing gear to replace it. The newer epoxies
combined with a light press fit should prove adequate, or you can
drill/ream a 1/8 or 3/16 diameter hole at the joint between the
shaft and gear and install a dowel pin as a round keyway.