Here is another take at estimating the brightness of the city lights as seen from the moon. As a starting point, let us try to estimate how much light is produced by the entire United States at night. (I would guess that this probably accounts for a significant percentage of the total light produced on Earth, and probably actually a majority of the total light seen if the Western hemisphere happens to be in view.)
This source: https://www.eia.gov/tools/faqs/faq.php?id=99&t=3 claims that the annual energy consumption used in the U.S. for "commercial lighting" is 141 billion kWh. This, however, includes both streetlighting and lighting of commercial buildings; let us guess that half of this goes to streetlighting, so 70 billion kWh.
Next we need to convert this to power. We divide this figure by one year, and also account for the fact that lights are on only half the time (only at night); so we multiply by 2. (In reality, lights are probably somewhat brighter in the evening than in the wee hours, so for peak output we might want to multiply by a larger number - but I do not thing this effect is very significant.)
To convert power to brightness, we need to multiply by the luminous efficacy. The most common types of lamps used for streetlighting are LED and sodium lamps; both seem to have a luminous efficacy somewhere around 130 lumen/watt, according to Wikipedia: https://en.wikipedia.org/wiki/Luminous_efficacy
To get the illuminance at the surface of the Moon, it remains to divide by 4pi (number of square radians in a sphere) times the distance from the Earth to the moon (roughly 400000km) squared.
Finally, to convert this to apparent magnitude, we use the formula given here: https://en.wikipedia.org/wiki/Illuminance
Putting the pieces together, WolframAlpha ( https://www.wolframalpha.com/input/?i=-+14.18+-+2.5+log10+%28%282%2870+billion+kWh%29%2Fyear++130+lumen%2Fwatt%29%2F%284*pi*%28400000km%29%5E2%29+%2F+%281+lux%29%29 ) gives a magnitude of about +0.7 - so among the top 20 brightest stars, but not among the top 10 (comparable e.g. to Betelgeuse or Aldebaran).
So this is definitely invisible during the day, swamped by sunshine and its reflection on the lunar landscape. Is it visible at night, next to sunlit crescent Earth?
I would go for "no". Here is a comparison point: the Earthlight ( https://en.wikipedia.org/wiki/Earthlight_(astronomy) ), whose magnitude is somewhere in the -2 to -3 range (source: https://iopscience.iop.org/article/10.1088/0143-0807/37/3/035601 ), and which, from personal experience, is definitely visible, but not so easy to spot.
Now the Earth seen from the moon is about 50 times brighter than the moon seen from the Earth ( https://astronomy.stackexchange.com/questions/8133/how-bright-is-the-full-earth-during-the-lunar-midnight ); while, if my estimate is correct, Earth's city lights seem to be about 100 times dimmer than the Earthlight on the moon, as seen from Earth...
OK, you would say, but then maybe during an eclipse?
Well, still unlikely. Consider that during a lunar eclipse (which corresponds to a solar eclipse on the moon), the moon is still visible; so there is still a fair amount of light reaching its surface. Seen from the moon, a solar eclipse looks like a dark Earth surrounded by the bright aureola of its atmosphere, backlit by the sun.
How bright exactly is it? Well, according to this source: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.487.136&rep=rep1&type=pdf (specifically Fig. 4), even in the deepest part of Earth's umbra, the illuminance is still no less than 10^-6 of the usual illuminance. In other terms, the Earth's atmosphere is roughly 10^-6 as bright as the sun, which corresponds to a magnitude of about -11. This is probably still bright enough to swamp the faint glow of the city lights...