In a way this entire discussion goes back to 100 AD give or take 200 years or so. The old Romans wrote about about lighting and crime. They incorporated anti crime elements in building design. The Romans more or less invented concrete, welfare, multi-story and multi-story apartment houses. They did not invent street lights.
A night time walk back from the wine shop or from dinner with Flavius Grusomnus could be a dangerous walk. No police, no lights, juvenile gangs, political gangs, MS XIII, upper class swells out for some fun, cut purses, foot pads and thugs, degenerates, poor people, illegals (yes they had them too) all in all very much like NY or Chicago or London or...
To make it worse the streets were often narrow, running between blank walls or ground floor business stalls that were literally empty at night, and in those streets there was offal stuff and more falling like the rain. No plumbing in those 4 story tenements so what came in through the door was going to transform and fall from above.
We all know that the Roman who could afford it traveled with light bearers and guards, others traveled in groups with lights, and in the better neighborhoods a man might walk with just a candle.
The primary purpose of the light was to avoid stepping in filth. The secondary purpose was to signal to any lurking bad actors the size and defensive state of the walkers. Thus allowing the bad guys to make an informed decision. So in that sense light deterred some crime. But you could just as well say that guards and weapons were the deterrent, an idea adopted by many.
The historical sources are anecdotes and biased because the writers were not poor or tenement dwellers. A 2000 year old problem and we still lack good data.
Then or now if lights deter crime what did the deterred criminal do? Did he or she simply select another target or seeing the light did the criminal repent and take up honest work?