how the hell did he allow the lions to kill over 30 people?

Well, I'm not sure if the exact number killed, but this movie is based on a real incident involving two lions eating a work crew in Africa. Been a while since I read up on it but you can find more on google. There were actually two lions that were taking men out of the camp in the night. After the lions were eventually killed, it was discovered that they were either sick or something to that effect. They chose man to hunt as we are way prey for them. A work crew made easy pickings for an African lion which is why it was like an epidemic

The lions were smarter.

The 40 people weren't killed in one night. It was over the course of many nights when the lions would sneak into the camp and pick off a man. These scene were supposed to be in the movie but were removed before the release. Patterson was only one man, and not a professional hunter. Many times when he would be guarding the north side of the camp, the lions would attack the south side, and vice versa.

Also the work on the railway line was quit big with the workers spread out over a large area. It wasn't very difficult for the lions to snatch a worker from the far end. Patterson couldn't be in all places at once. Also his gun misfired a couple of times.

Also in real life, Patterson tried a number of tactics, like using a goat bait but the lions didn't fall for it. They were smarter than your average wild beast and it was their cunning which allowed them to kill so many people. It was precisely because of this behavior that the locals thought that they were not lions.

"I'm the dude, playing a dude that's disguised as another dude".