The lawyer might suggest others and the client may or may not contact them. Once a criminal case has actually started a lawyer needs permission from the court to leave. Often that permission is not given. I believe Trump's supposed problems with his legal team have been overstated like other aspects of this investigation. The main problem he has is that he doesn't want to accept legal advice that is contrary to what he wants to do. Some lawyers can work with a client like that and some won't do it.

Trump must be the most difficult lawyer in the world!

Why does the court have approval over a lawyer leaving once a criminal case has begun?

First, it will delay the case while the client gets a new lawyer and that new lawyer has to get up to speed on the case. Second, a client could use that as a tactic to delay the case and thus cause undue hardship to potential witnesses and/or the victim in the case.

or simply not in his best interests, it might be an ethical concern to suggest another lawyer.

It should be, I guess.

Thanks for your thoughts.

There is no obligation to provide a referral.

If a lawyer has been representing a client in a court proceeding, then permission of the court would be required for the lawyer to withdraw.

But, no, the 13th Amendment still applies.

13th Amendment!

Thanks for the answer to my question and the chuckle.

...then you get a little sensitive to that fact.

Nobody ever has a Constitutional right to a dentist, a plumber, or an auto mechanic, as I am often reminded.