Unfortunately, it is a PowerPC application, which isn't supported in Mac OS X Lion 10.7.5. You could however run it under Windows via Boot Camp, Parallels, or Fusion. That would require the purchase of a copy of Windows XP and Parallels or Fusion if you went that way. Total cost would be $100-200. It would also require a bit of setup. Not sure if that would be worth it just for one older game.
So I should buy a PC for my next computer?
I have a 2005 Mac laptop that I currently use for Oregon Trail. How long can I possibly maintain it, and under what conditions?
What is the best way to be able to play Oregon Trail for years to come?
You can buy a PC if you like, but that's your decision.
I still use Macs that are older than that, so it should work until the hardware fails. Two of the Macs that I use the most are a 2006 Mac mini and a 2007 MacBook Pro. You will be limited to what you can do however, due to the age of the OS and other software installed. You can continue to play OT as long as the computer works.
There is a newer version of OT, but it is a sequel to the older versions and the game play will be different.