Hydrocarbons will likely be in short supply on the moon but if there is, say, a zinc mined, it could be "burned" in zinc-air cells.
The biggest challenge to the obvious solutions - either solar plus lots of batteries, or nuclear - would be to crack water into oxygen and hydrogen, and then burn them during the night. The challenge there is storing the hydrogen. But if you do that, basically what you'd be doing is using hydrogen/oxygen as an energy storage mechanism, e.g. as a battery. You'd need to use solar during the day to crack the water.
12% by mass is iron, with calcium, aluminum, magnesium at 7-8%. These could be considered ores worth mining on Earth. All four metals readily burn in oxygen, even though aluminum needs some help igniting.
There are various studies to have stuff survive lunar night without a nuclear source, and it takes on the order of 10kg of stuff to keep a 1kg payload alive. And in turn that takes 100kg of spacecraft/fuel to fly it all there. That’s not including the rocket and its fuel to get to Earth orbit first.
Solar panels should be able to provide the necessary energy which can be stored in piles of rock and insulation should be able to to prevent the loss.
The 'article' says that the lunar night is rife with problems but doesn't mention what they are. There is no weather after all.