You may have permission problems with your Aperture Library or a problem with corrupted user preferences.
Try the Aperture 3 Trouble Shooting Basics, and start with removing the user preferences "com.apple.Aperture.plist" to the Desktop after quitting Aperture.
In Mac OS X Lion your User Library is hidden by default.
You can access it by using the Finder's "Go" menu from the Finder's main menu bar.
- Select the "Go" menu entry and hold down the "alt/option" key ⌥, until the library appears in the drop down menu.
- Select and click "Library".
- In the window that opens select the "Preferences" folder, and then move the file "com.apple.Aperture.plist" to the Desktop, like Kirby suggested.
Make sure, you quit Aperture properly, before you move the preference file. Im Mac OS X Lion new process system (automatic termination) the only safe way to ensure that an application really quits is to log off and on again.
If removing the preferences does not help, try the "Library First Aid Tools" and repair the permissions and repair the database as described in the link above.
Regards
Léonie