Not an American but have been involved in lots of US legal things for a charity. Generally "their lawyer" refers to a lawyer (solicitor in British usage) who is 'on retainer', which means that the client either pays a monthly fee to secure the lawyer's availability, or has a deposit with the lawyer which will be drawn from if legal assistance is needed.

Funnily enough, Americans do not use the term solicitor; that's reserved for lawyers working for the government!

> Funnily enough, Americans do not use the term solicitor; that's reserved for lawyers working for the government!

It is certainly a rare term in American English. I associate it with the probably now-archaic "NO SOLICITORS" signs, which used to be commonly used in an effort to ward off door-to-door salesmen and such. The specialized usage you are referring to is the use in titles of certain important government lawyers (I'm only aware of this in the federal government). The most famous is the Solicitor General, which is an appointed official in the Department of Justice whose job is mainly to argue on behalf of the government before the US Supreme Court.