No. He can fire him if he thinks it is grounds for fair dismissal, he can decide not to extend his contract, he can call him out in private if it's affecting his performance, but he absolutely cannot divulge his private life
Well, he clearly can divulge that private life stuff... because he just did.
In a way this is a circular topic because we go right back to what I said yesterday, i.e. none of this matters. There's nothing "inadmissible" "unacceptable" "intolerable" here... because there's no one stopping Lefevere from saying whatever he wants.
I noticed some people on social media throwing around talk of defamation etc. but the legality is very sketchy & probably not a can of worms Alaphilippe & his people want to open.
In the end there's just a basic matter of sense, i.e. relating to the question "does throwing a rider under a bus work as motivation, or demoralization?" There's some José Mourinho modus operandi & school of thought in Patrick Lefevere's tactics, IMO.