If you cannot source the part, you may be reduced to measuring the broken parts and then making a new one, always supposing that
a) The lathe is operable without the failed component
b) You have access to a mill.
Although if the lathe is operable, mounting the raw material on a vertical slide, or in the toolpost, with an end mill in the chuck. The first side should be relatively easy, but because of problems holding, the second side will be more difficult, certainly looks to me like some light cuts, .
If all else fails, throw yourself on the mercy of a local Model Engineer!
Best of luck!
Howard