Hi!
Once you've added a map to a layout using a map frame, you can change its projection.
To do this, right-click the Map in the Contents Pane and choose properties
Then adjust the coordinate system on the Map Properties window that appears. It is important to know that if you change the map coordinate system in the layout, it is also changed in the map view and vice versa. Map frames on layouts just reflect the map.
Cheers,
Aubri