So, same principle, for the wood lathe :
For this one, I simply drilled a 12mm hole in the simplest tool rest I have, made of a single vertical pole, see the spot tool rest)
Using a little brass pin in the chusk to set up the heigth with the live center :
And not forgetting the drop of oil !
See also the depth stop, bottom left.
And for this one, as a bonus, you will have a video :
(you will be able to practise your french by the way)