Mark V Lawson was educated at Belfairs High School in Leigh-on-Sea, Southend Technical College, York University and Cambridge. He received his BA in Mathematics from York University in 1981, studied for the Part III at Sidney Sussex College, Cambridge, and then returned to York to work on his DPhil under the supervision of John Fountain. During this time, he was also a part-time course tutor for the Open University. His post-docs took him first to Lincoln College, Oxford for three years as the Thomas Rotherham Junior Research Fellow in Mathematics, and then to the Technische Universitaet, Darmstadt to work for a year in Karl H. Hofmann's research group supported by a Royal Society European Exchange Scheme Programme Fellowship. In 1989, he returned to Britain to take up a lectureship in mathematics at the University of Wales, Bangor. In 1999, he became a Senior Lecturer in Mathematics at Bangor, and in 2004 he moved to Heriot-Watt University, Edinburgh to take up a lectureship. He was promoted to senior lecturer in 2007 and professor in 2015.
Lawson has published over 70 papers with his research interests centred on algebraic semigroup theory. He has made research visits to Australia (1992, 1994), Hungary (1996), France (2016, 2018), Germany (1996, 2012), Portugal (1998, 2001, 2008, 2010, 2012, 2016, 2018), Israel (2000, 2009) and Canada (2000, 2010, 2012, 2016). Seven research students have successfully completed their PhDs under his supervision: Peter Hines (1998), Helen James (2000), Tanveer Khan (2001), Joseph Matthews (2004) , David Gareth Jones (2011), Bassima Afara (2013) and Alistair Wallis (2013).
His book Inverse semigroups: the theory of partial symmetries was published by World Scientific in 1998 and has been well-reviewed. He has written three other books: Finite automata, published in 2003, Algebra & Geometry: an introduction to university mathematics, published in 2016 and A first course in logic, published in December 2018. He has also contributed chapters to the Handbook of networked and embedded control systems edited by Dimitrios Hristu-Varsakelis and William S. Levine, published in 2004, and to Wagner's theory of generalised heaps by Chris Hollings published in 2017. In 2003, he carried out research for DSTL on automata theory. He has been one of the communicating editors of Semigroup Forum since February 2011, and between 2005 and 2013 he was one of the algebra editors for the Proceedings of the Edinburgh Mathematical Society. In 2011, he was awarded the Graduates' Teaching Prize at Heriot-Watt University. In 2017, he was awarded the Mahoney-Neumann-Room Prize by the Australian Mathematical Society.
Currently, he is first year co-ordinator in mathematics. Previously, he was a member of the University's Discipline Committee, the Undergraduate Studies Committee and served two terms as a member of Senate. In 2017, he completed three years as pure mathematics external examiner for NUI, Galway having previously been external examiner for pure mathematics at the University of Newcastle for four years until 2013 and sub-honours external examiner for mathematics at St Andrews University for three years until 2014.