On 21 March 2024, Lynne was appointed Cabinet Secretary for Education, and on 11 September 2024 was re-appointed as Cabinet Secretary for Education.
Ar 21 Mawrth 2024, penodwyd Lynne yn Ysgrifennydd y Cabinet dros Addysg, ac ar 11 Medi 2024 fe’i hailbenodwyd yn Ysgrifennydd y Cabinet dros Addysg.