The lamp protested its forced retirement by damaging the wall on its way out. I patched the damage, but it's difficult to discreetly patch a textured wall.
Replacing the lamp with an overhead light would have been ideal, but there is no light fixture or switch in the laundry closet. There is just one electric outlet behind the washing machine. Thus I needed a plug-in lamp.
As it happened, I had a pair of wall-mount lamps that I purchased from IKEA some time ago but could never decide where to use. They would finally find a home in the laundry closet.
Taking advantage of the lamps' extra-long cords, I was able to mount them to the wall above the closet doorway so the light would shine from above, almost like an overhead light.
Each lamp has an on/off switch on the cord. I used mirror clips to hold the cords so that the switches would be easily accessible. I just have to reach up right inside the doorway to flip the switches.
I ran the cords across and down the wall, then across to a small power strip I mounted on the wall near the electric outlet.
I used a plastic cord channel to house the cords running across the wall.
Painting the cord channel to match the wall disguises it nicely. A raven plate hides the huge patch on the wall, and some fabric hides the power strip.