How does the lighting in this photo work? It is strange.
This is the Apollo 11 photo designated AS11-40-5925, a popular shot with moon landing deniers.
The camera is facing generally north-north-west. The sun is low in the sky, about 10º-15º above the horizon on the east. The silver pole in the upper right of the photograph is pretty much straight up, casting shadow in the expected direction. The landing leg in the upper center is tilted away from the sun angle somewhat, not enough to significantly change the direction of the shadow. This is all really straightforward.
The confusing part is the probe in the right foreground. These probes hang down from the footpads of the lander, and when one of them touches the lunar surface, they activate an indicator in the cabin, alerting the crew that the LM is within about 2 meters of the surface. When the pad comes down to the surface, the probes are bent away in unpredictable directions depending on which way the LM is drifting at touchdown, as discussed in this QA.
In this image, the probe is bent outwards, generally toward east-north-east. The probe extends out of frame to the right; it's about twice as long as the diameter of the footpad. Since it's mostly pointing towards the sun, the shadow is severely foreshortened -- the shadow is cast nearly down the length of the probe. That’s why the angle of the shadow appears so different from the others.
Here's a quick reproduction of the situation with a couple of chopsticks stuck in a piece of styrofoam, lit by a single light, with shadows appearing to fall in very different directions:
It’s not a perfect match for the Apollo photo —- it’s taken from a higher angle. However, it does demonstrate that the direction the probe points can drastically change the direction the shadow extends over the surface.
Here's what the configuration looks like from above with additional lighting:
NASA has no explanation for Karloff the giant moon cat, however.