MediaFire gave you a bunch of redirects? That's really peculiar; it should be a direct download link that just gives you the file. I just tested it and it worked great in FireFox. I'm not sitting on my Mac, so I can't test it in Safari, but that's always worked fine in the past.
What version of OSX are you on, just for reference? You might try hitting Show Package Contents when you right-click (or command-click) the application. Then look under Contents, MacOS, and run the executable in that folder that's appropriate for your OS (Intel, PPC, etc). Sometimes OSX can get wonky about the permissions of the actual app bundle with downloads in general, but I've never seen this specific problem. I'm wondering if this issue is specific to the version of OSX you're on, or something along those lines, which is why I suggest this and ask what the version is.
LotS has been out since January, with a few thousand downloads, and this is the first report I've had of this issue. So either it's something that changed in OSX, or else something must be wonky with GamersHell. You might try giving the MediaFire link another try, or a try in Firefox, and that ought to solve the problem if it's GH. If that's what it is, I can let the GH folks know so that they can fix their version.
Sorry for your frustrations, there -- we try to provide lots of mirrors so that you're assured of being able to get your files any time you want, even if something should ever happen to us (and, of course, it helps us on bandwidth costs, too -- mediafire we pay for, the others we do not). As another alternative, if you use Steam for Mac, you can always plug all your license keys into Steam and it will do all the downloading and installing for you. If you don't use Steam for Mac, of course, that's quite all right as well -- we don't expect you to or anything like that.
Hope that helps!