WELL...the light that was used, the main or key light is a hard light source...in those days, probably a 16 to 20 inch "pan reflector" or parabolic reflector...something that throws a crisp, hard-edged shadow. You can see the shadows from her eyelashes, nose, and also, not the very strong and BIG lower lip shadow! As you can tell, a light that would create that tall a shadow of the lower lip must have been up, overhead, and fairly close to her...the main light is "raining down" on her from about what would be called "12:30".
In each eye is a very small, bright dot of light...that is from a small light source. At that size, I'd say something like a 5 to 7 inch round reflector; I use something similar but in 11 inch, it is larger, so I am gonna say it's a small light...
With a good, smooth makeup foundation, and some high quality powder on top of the base, you can shoot this and in B&W it will look a lot like this....this is not a fancy lighting setup--a good part of it is the carefully done hair, the pose, and very exacting light placement, and of course, lauren Bacall's gorgeous features. Look again at the lower lip's shadow, but also look carefully and notice that the TOP lip throws a shadow on the lower lip!!!
This could actually be done using sunlight as a hard, crisp overhead source. These days there is this irrational fear of hard, crisp-shadow lighting. This photo is a perfect example of how to do crisp, hard-edge shadow lighting.