Yes. At least, non-legal professionals acted as lawyers.
Courts in Harry Potter seem to operate using a jury system. The Wizengamot is summoned to hear a trial and pass judgement on individuals. There are no judges and the person presiding over proceedings is either the Head of the Department of Magical Law Enforcement (as was the case in the trials Harry saw in the Pensieve), the Minister of Magic (as was the case in Harry's trial) or the Senior Undersecretary to the Minister (as was the case in Deathly Hallows). There seem to be certain people who are allocated as Interrogators.
Interrogators: Cornelius Oswald Fudge, Minister for Magic; Amelia Susan Bones, Head of the Department of Magical Law Enforcement; Dolores Jane Umbridge, Senior Undersecretary to the Minister.
(Order of the Phoenix, Chapter 8, The Hearing.)
In the absence of formal solicitors these Interrogators seem to take on the function of barristers for the prosecution. They summon and question witnesses, try to build a case against the accused and seem to have an interest in securing a conviction. Of course, since we only have a limited number of examples within the books it's difficult to draw any firm conclusions. In each trial in the books the Interrogators are predominantly disciplinarians who have a vested interest in convicting the accused. It's clear that they are not neutral judges, however.
We also have the example of Dumbledore.
"Witness for the defence, Albus Percival Wulfric Brian Dumbledore," said a quiet voice behind Harry.
(Order of the Phoenix, Chapter 8, The Hearing.)
He may describe himself as Witness for the defence but he is obviously not acting as a witness since he wasn't there for the Dementor attack. He acts more as a defence counsel, riposting the arguments of the prosecution and seeking to prove the innocence of the accused. None of the other court cases feature any such defence counsel, from which I would say that a defence barrister was optional and only rarely used. After all, if a wealthy, young Quidditch star like Ludo Bagman seemingly defended himself then professional defence lawyers were obviously not the norm. As a matter of course, the accused would just answer the Interrogators' questions - although there was a Charter of Rights that allowed those who were defending themselves the right to call witnesses in their defence.
"I may be wrong," said Dumbledore pleasantly, "but I am sure that under the Wizengamot Charter of Rights, the accused has the right to present witnesses for his or her case? Isn't that the policy of the Department of Magical Law Enforcement, Madam Bones?" he continued, addressing the witch in the monocle.
"True," said Madam Bones. "Perfectly true."
(Order of the Phoenix, Chapter 8, The Hearing)
None of these individuals could be claimed to be professional, full-time lawyers (although Dumbledore was a former Chief Wizengamot). They are teachers, politicians and bureaucrats. But within the fairly informal legal setup in Harry Potter they perform the roles of lawyers within the court. So whilst, no, there isn't anyone that I'm aware of in Harry Potter that is a dedicated legal professional various characters function as lawyers when serving in the Wizengamot is part of their wider duties.