Does " two lights" mean " two traffic lights?"

Yes, it probably means his car was a couple of blocks away sitting at the second set of lights. The red and white lights are on a police cruiser.

In China red lights are for "reference" only. In the West , we obey the signals (mostly)

Thank you.

"Berkley the first right after that" refers to "(turn to the left, and then ) to the right, there at the first traffic light is Berkley"?

Yes. Our government used to be the first to show contempt on the law they grandly made.

Wilshire was two lights down on the left, Berkley the first right after that.



What the text means is: Standing at a point looking down some generic street/road, Wilshire was two traffic lights distant, at right angles to that street/road. Then the next street you would come to after crossing Wilshire was Berkley.

But that doesn't seem to match the map, assuming that this is Wilshire Boulevard and Berkley Street in Santa Monica, CA. Berkley Street runs at right angles to Wilshire Boulevard.

Google "map wilshire boulevard and Berkeley Street".

K, upon rereading the above, I'm not sure if this quote is referring to people or a place. If it's people, then the first one is driving or walking and is near or about the second set of lights. The other person is one block ahead of them.
If it's directions.. then I'm assuming there is more to the story and Wilshire would at the second set of lights, and Berkley is one block ahead.
We drive on the right hand side of the road here in N. America. So this would be a right hand turn. If this was in England, then yes, you'd have to turn left then right.

Just saw your post. Yup, totally misread that. Context is important.

Not sure what you mean by this. In the United Kingdom we drive on the left, and so do a fair number of other countries. We have many intersections where you can "filter" - turn across oncoming traffic - which is held up at a certain part of the traffic light cycle, (you get a rightward pointing green arrow) so I don't understand the part about turning left then right. None of our cities are laid out in rectangular or square blocks; I don't know if that makes a difference?