Monte Carlo might be ok to OTC derivatives, however for automatic market making of exchange traded option, which are mostly American, it would be too slow.

After a bit more googling, I found these more recent slides by Jesper Andersen, where he believes that the Leif et al method could be extended for local vol (see page 25): https://www.cqfinstitute.org/sites/default/files/4%20-%20Jes...