Anderson, England’s all-time leading wicket-taker, held talks in April with Test coach Brendon McCullum, captain Ben Stokes and managing director Rob Key.
The hierarchy’s decision to move on from Anderson is partly fuelled by a desire to plan for the next tour of Australia, in the winter of 2025-26, when Anderson will be 43.
Off-spinner Lyon sits seventh on the list of leading Test wicket-takers, four places behind Anderson, and the two have played against each other in 22 Ashes matches.
“My care factor for England is pretty low, but I was pretty surprised when I did read that they tapped him on the shoulder,” added Lyon.
“I look at James and what he’s been able to do for England cricket, it’s pretty remarkable. This is just my opinion – I still think he would be England’s best bowler.”