Lynne was a member of ACME from 2009 to 2013 and again from 2017 to 2020, and sits on the Royal Society Partnership Grants Panel. She is active in various mathematics education communities including as chair of governors of the Cambridge Maths School, trustee of National Numeracy and MathsWorlduk and fellow of the IMA and ISDDE. She was President of the Mathematical Association in 2014/5 and is a member of the Executive committee for the proto-Academy for the Mathematical Sciences.
Lynne is the author or editor of many books and articles and is well known as an international conference speaker and professional development lead. In 2022 she was awarded an OBE for services to education.