If the Moon was actually a giant mirror-lens thing that was the size of the Moon, but perfectly shaped to reflect and concentrate sunlight shining on it into as small an area as possible on the Earth's surface, you'd start a fire with that very easily. Probably turn a county-sized area of the crust into lava or something actually.
On the other hand, if the Moon was a perfect reflector, but a big sphere/hemisphere pointed at the sun, then it would receive a lot of high-energy radiation, but reflect it back out in every direction all over the universe. I'm not sure of the math for that offhand, but it sounds difficult to concentrate it back to something even as concentrated as direct sunlight. I suppose it would involve considering the fraction of the total solid angle the reflecting area of the Moon would shine at. Even the entire Earth's surface would be a really tiny fraction of that area, so sounds impossible to concentrate things back to fire-starting intensity.
Assuming these scenarios are basically right, then the actual Moon is a lot closer to the second than the first. So starting a fire isn't practical with any lens system you could build on Earth. Maybe you could build some massive mega-lens thing in space near the moon that concentrated enough of it back on the Earth to be near-sunlight brightness. Or just set up a more manageable sized reflector on the Moon itself, or in space, to reflect sunlight in a more concentrated way to a small area on the Earth.