This may be a problem of an unreadable Aperture preferences file:
Try the following:
Remove the Aperture's user preferences from the User Library as described here:
Your User Library is hidden by default in 10.7.5 - to open it in a Finder window use the "Go" menu from the Finder's main menu bar.
- Quit Aperture, if it is running. Log off and on again.
- Open the user library by using the Finder's "Go > Go to Folder" menu and hold down the options-key, until "Library" appears in the drop down menu. Select it.
- In the widow that will open, scroll down to "Preferences"
- From the "Preferences" folder remove "com.apple.Aperture.plist".
Then try to launch Aperture again.
But deleting the "Preferences" file will cause Aperture to forget the preferences settings. Be prepared to have to reset all options you set using the Aperture Preferences panel.