Can this WWII era rheostat be modified to dim an LED bulb?
Reducing lamp voltage will dim the lamp.
I suspect that any LED lamp will draw so little current that you won't get much of a voltage drop. If, for example, you have a 24 V, 6 W lamp you will draw 6/24 = 0.25 A. The 50 Ω resistor will drop approximately 50 x 0.25 = 12.5 V and that should be quite enough. (You can recalculate for any other lamp.) The effect may not be linear because the relationship between current and voltage on LEDs is non-linear.