Fitzsimons joined AIG in July 2019 and was most recently serving as the insurer's chief administrative officer.
Lyons will move into the newly created role of Global Chief Actuary and Head of Portfolio Management at AIG from January, after which Fitzsimons will take his place, the company said.
AIG's board last year approved a plan to separate its life and retirement business, which sells insurance and annuities.
The insurer plans to use an initial public offering to sell part of the business, in which Blackstone Group has agreed to buy a sizeable stake.
AIG also named company veteran Elias Habayeb as CFO of the unit, effective immediately. Habayeb was most recently the chief financial officer of AIG's general insurance business.
(Reporting by Amruta Khandekar; Editing by Devika Syamnath)