Lynne has been the Head of Mathematics Solutions at Cambridge Partnership for Education, Director of Cambridge Mathematics, Director of NRICH and PI on Underground Mathematics. She was President of the Mathematical Association and Executive Chair of ISDDE.
Lynne is an ex officio member of ACME as chair of the Academy for the Mathematical Sciences Education workstream. She was also a member of the Mathematical Futures Programme writing group. In 2022 she was awarded an OBE for services to education.