OK, this seems weird to me. When I am exporting on LR I clearly have the resolution set to 240 ppi. However, when I look at the photo info is says it is 72 dpi...? I can not figure out why. How do I fix this or am I reading something wrong?

I just tested mine. Exported at 300 dpi and it said 300 dpi in CS4 when I opened the exported file.

It depends where you're reading the "photo info" but it really doesn't make any difference. The thing you're interested in is the height and width pixel dimensions. There's nothing to "fix".