can a lawyer tell anyone outside the client what the settlement amount of a out of court settlement

It depends on the terms of the settlement. Some parties want to keep the terms confidential, in which case the settlement agreement imposes secrecy on the parties.  That is common in commercial and employment disputes. Most parties to personal injury cases in NY do not bother with confidentiality. If a lawyer won't tell you the amount, it's probably because its confidential. But just because a laywer may tell you, doesn't mean he or she will. If someone asked me how much a client received in a non-confidential settlement, I imagine I'd tell them to ask the client unless I specific authority to speak on the subject.