You didn't read what he said. There's no mixers on lightning.

They need to update their tech. CJs were an okay measure before lightning got to where it is.

You have privacy on lightning as long as: -you run your own node -You trust and verify your peers -You trust they won't close your channel this revealing your channel information on chain -you have faith that you aren't being targeted for probing or timing attacks I bet you secretly worship lightning in private devotion to come out with that much faith in it's privacy.