1) It could have been some small, local earthquake (which maybe shouldn't even be considered a typical earthquake, maybe more of a mudslide that destroyed the tracks)
2) We don't know how far Grimwood station is from the landslide site. Maybe it's several dozen kilometers/miles away, and the landslide occurred when Lily was already in Grimwood. Perhaps a possible earthquake could have been less felt there.
I live in the UK and we never have big earthquakes here. The last one one which was about 4-5 on the Richter Scale was about 100 miles away, and it still caused my entire bedroom to shake and woke me up. I think if it happened a few dozen kilometres away, they would have definitely felt it, and the train would have stopped. Even that would have caused enough commotion amongst the other passengers to wake Lily up, even by some miracle she'd managed to sleep through the earthquake.
But when Lily is talking to the old woman, on the first night, she says the earthquake caused a tunnel to collapse, which suggests it was a bit more than just a minor quake. In fact, in an earthquake prone zone, you would expect train tunnels to be built to withstand anything that wasn't a major quake.
Also, the following day when she's talking to a random guy in an alleyway, he mentions that the earthquake caused landslides that blocked the road as well. So in the good ending, how did her parents manage to come pick her up by car? As things stand the good ending is impossible, and she's completely stranded in the town either way.
I'm not saying the initial set-up via the earthquake is wrong, just that it needs to be explained in a somewhat more logical way. The guy in the alleyway, just needs to talk about the rail tunnel collapse, and not mention roads at all. Lily could have been awoken by the effects of the earthquake, when the train stopped at Grimwood station. She could have been asked to disembark and later informed that an earthquake had taken place, and a tunnel between Grimwood and New Georgetown had collapsed, stranding the train in Grimwood station. It's that simple.