Depending on how much lift you want to allocate to getting the installation set up - solar photovoltaic and solar thermal will both work just fine, especially with a capacitor farm. Remember, solar works a lot better up there than it does down here.
You can reduce the immediate instantaneous power demand by setting a lower acceleration rate and using a longer track.
Even if you can gradually get the velocity up to the 7,800 fps velocity to escape the moons gravity, it's still a huge amount of energy needed and the energy needed is the same even if you can spread out the consumption of the energy over time.
They're making a lot of estimates, since it wasn't a controlled experiment, but looking at the wiki info on the 2013 meteor in Russia, they estimate it had a mass of over 10,000 tons and had kinetic energy of 400-500 kilotons. A mass of 100 tons would be 1% of that meteor so would extrapolate to kinetic energy of 4-5 kilotons. That's 1/3 to 1/4 the energy of either the bombs we dropped on Japan. I think that Hiroshima was 15 kilotons, Nagasaki was 20.
So lets say that to equal one WW II era nuclear bomb you'd need to get over 300 tons of mass up to the lunar escape velocity of 7,800 feet per second. 300 Tons is more than 100 Chevy Suburbans.
Sunlight in space carries the energy of 1,367 watts per square meter (and photovoltaic energy capture is far from 100% efficient, so the actual energy available is much less). The infrastructure needed to capture and store the amount of energy needed to accelerate 100 SUVs up to a velocity of a mile and a half per second would be huge. Just to equal a single WW II bomb. And then you have to go back to capturing and storing sunlight again, recharging the batteries so you can take another shot. While any location on the moon spends half the time in darkness.
How much manpower and money would have to be committed to get something like that weapon installed in a hostile extra-terrestrial environment? And what would it get you? You aren't going to be able build it without somebody noticing and considering what risk it might pose. And if somebody started launching attacks against the US or Russia or China from the moon, I'd bet the response would be the total destruction of the weapon within a couple of weeks. It's a hell of a lot easier to destroy something like that than to build it. With a number of lasers synchronized we could probably knock it out from earth without even having to launch a guided missile to blow it up.
All in all, it's just a silly idea that is fun to contemplate while reading the musings of a science fiction writer, but something that will never, ever get built.