In VFR conditions, no there is no restriction against landing in an airport where runway edge lighting or other airport lighting is not lit at night. That being said, without any visual references, it may be very difficult to locate where runway is or judge or hide above the runway in order to land. In addition if additional lighting is not available i.e. glide path lights, approach lighting, etc. is not illuminated. With absolutely no airport lighting visible, you’re going straight into a black hole and maybe in very real danger of striking obstacles or a CFIT attempting this.
If you have approach lighting in glide path lighting, you can land with relative ease, provided your aircraft is equipped with landing lights. I found this out early on in my flying experiences, where I once landed at Ponca City airport (KPNC) at night. The PCL system would only activate the approach and PAPI lights but the REL would not illuminate. Using the approach and PAPI lights gave me a guidance to the runway, which was illuminated enough by my landing lights on short final to properly judge and execute the roundout.
The same basic rules apply on an instrument approach. That being said, §91.175 (c) prohibits a pilot from descending below the DA or MDA on an approach without the runway, it’s markings, or runway lighting being visible. This is extremely difficult to do at night on an instrument approach without proper airport lighting operating, it would almost certainly require a missed approach be executed. But who knows maybe you got a pair of LoPresti Moonbeams that turn night into day on a straight in approach, illuminating the runway from far away enough to make it visible above the DA or MDA on a straight in approach.
Now the real question becomes one of risk management. That is, even if you can’t do this under the law, it probably is unwise to actually do so. Which one is wiser: Attempting to land here, or remaining airborne and flying to another nearby airport which has working airport lighting and land there?