Hi. Harry, nice observation and you are correct.
Brick lintels should always be primed at the minimum to prevent rusting and galvanized would be a luxury but ideal.
This is what happens when steel lintels don’t get primed and painted.
I could also not resist to notice from your pictures that there are no weep holes visible nor evidence that the flashing was installed.
Brick lintels should not be caulked as I see in the photo, that dams up water on the lintel and leaks and/or promotes rusting. In cold climates would present blowouts in some instances.
Also I observed that the window unit is not sealed to the brick.
This is always a recommendation due to the unknown flashing details behind the brick. It also allows water intrusion in the brick cavity, which in this case with no weep holes could and possibly be a potential problem.
Hope this helps a little.