It is the first time they meet ministers since the start of their union action.
Lawyers in England and Wales have joined an ongoing strike since their row with the government over pay has intensified.
Lewis, who was appointed two weeks ago, said talks had been constructive and would continue.
But who is the new Attorney General Brandon Lewis and what does his role entail?
Who is Brandon Lewis?
Lewis became Lord Chancellor and Secretary of State for Justice on 6 September 2022.
He was previously Secretary of State for Northern Ireland from 13 February 2020 to 7 July 2022.
He was elected Conservative MP for Great Yarmouth in 2010 and was appointed CBE for political and public service in September 2019.
Outside of politics, Lewis is a qualified attorney and a corporate executive.
After receiving his degree in economics and law from Buckingham University, he went on to study commercial law at King’s College London.
Before joining government, Lewis served on the Brentwood Borough Council for over 10 years and was leader of five of them.
He was an active member of a number of all-party parliamentary groups, including those for business zones and local growth, as well as for local government.
The 51-year-old’s work sometimes focuses on coastal erosion, and he continues his work with colleagues representing other coastal cities to address common issues in their constituencies. He is married and has two children.
What are his responsibilities as Minister of Justice?
Lewis’ responsibilities, which include overseeing all Justice Ministers’ portfolios and Justice Department strategy, as well as the Department’s Covid-19 response, supported by ministers according to their portfolios.
He is also responsible for international affairs and future relations with the EU, support to the Department of Justice for the UK countries, judicial policy including on wages, pensions and diversity, as well as business services.