That's pretty weird! Do you know if there's any reason why your machine would be running a 32-bit kernel? I didn't think that was still supported on Lion...
It's a 2007 MacBook, with a Core 2 Duo processor. I had been under the impression that it was running a 64-bit kernel. But it seems I was wrong. I believe that since Lion most Macs boot with a 64-bit kernel. I guess this model was left out.