I might be able to help you as I had exactly the same error message after upgrading to the latest version of iPhoto on Lion 10.7.2 but iPhoto would then also crash (quit unexpectedly) after about 1 minute. However I seem to have just fixed it as follows:
1. Launch iPhoto with the Option key depressed and create a new library. See if that opens and runs OK.
2. With iPhoto still open and displaying the new blank library, open Finder and locate your original iPhoto Library and open it.
3. Choose to relaunch iPhoto with the original library and you will see the same message as before - "iPhoto has detected inconsistencies in your library. Click repair to avoid problems." - Click Repair as before.
When I followed the above my original library then stayed opened without issues and iPhoto stabilised.
You may just be able to perform the first step then close iPhoto and then open the original library (hold down alt whilst launching iPhoto to choose the library, or click on the library in Finder) but thought I would detail exactly what I did in case it makes a difference.
Hope this works for you too
Regards
Tim