Lawyer is someone who practices law - it can include academics
It really isn't. It's basically a meaningless layman's term. Academics teach or research law - they do not practice law unless they also happen to be a solicitor with a practicing certificate or a member of the Bar or the Faculty of Advocates. Parr time tutors are often practising solicitors, barristers or advocates- full time academic staff are unlikely to be practicing.
Am I right in thinking you can't call yourself a solicitor or barrister or doctor without the relevant qualifications? Interesting that lawyer isn't covered
A solicitor must have a practicing certificate from one of the Law Societies. An advocate (Scottish version of barrister) must be a member of the Faculty of Advocates and an English barrister a member of their equivalent. All of these people will have gone through a qualifying process and are regulated by their professional bodies, who in turn are regulated by statute.
"Lawyer" isn't covered because it's a meaningless term in a professional context.