It's sounds like you're just getting aquainted with Windows 7 security defaults. Generally speaking (and I do mean "generally"), MS now wants you to put your data bases/files in directories like "Documents" or "AppData" going forward AND to "help" us with this, they've changed the directory defaluts among other things. If you can, relocate your DB's. And naturally, there's a down side. AppData, which can be referenced directly via C: etc. has some odd characteristics...like it's invisible and you have to set bits to see it. Documents is pretty good but it can be relative to the domain environment. We ship computers/evironments with our product so have the luxury of being able to force our customers into particular directory structures.
If you really want to install your app including db in the Program files or PF x86 directory, you'll have to change the directory security to read/write as the default is now (with Win 7) read only. This is a lot trickier than it sounds and quite frankly we only did this manually a couple times and after agonizing our way through it, we decided that we'd do what MS wanted us to. (To give you a heads up, you'll change directory security in Windw Explorer and it will lie to you and tell you that you've changed it. BUT if you run your app or return to Windows Explorer, you'll see it didn't chage the setting. Next time my users piss me off, I'm writing something like this myself.) Sqlite is apparently (from our experience and deduction, not looking at the source code), seems to be subject to the directory settings in which it is located...which of course makes complete sense. You can google how to change the security for the directory but it's tricky. AND our experience is that if you add a new user to your machine, the directory security gets reset.