Michael,
2) I still do not understand what you mean by "repair." I have opened my iPhoto '09 version 8.1.2 in Lion and I do not see any menu item labelled Repair.
iPhoto has built-in library First Aid Tools. They are are nit visible in the menus, but you launch them by holding down the key combination option-command while launching iPhoto. They look a bit different for each version, see: https://support.apple.com/en-us/HT201769
There are several repair options. As a precaution I'd use the ones with "repair" in the name, not the rebel ones.
1) I have not yet opened my iPhoto Library with version 9.6.1. This version will not run in Lion.
I want to maintain one set of iPhoto Libraries for use in each of these versions of OS X.
When I do so, will the Library created by this version of iPhoto '11 continue to operate with iPhoto '11 for Lion? If not, then I will probably only use iPhoto '11 in Lion and not upgrade it for version 9.6.1 in El Capitan until I am forced to do so.
Generally, any version of iPhoto '11 can open libraries created by earlier versions of iPhoto '11 and iPhoto '09. So you can open your iPhoto 8.1.2 library in any version of iPhoto '11. But as soon as you open it in a newer version, it will be modified, so the older version of iPhoto can no longer read it. You will have to take care to copy the libraries before opening them in a newer version. Always start iPhoto while holding down the options key, so you are presented with the library chooser panel.
If you are working on photo books, finish them in the version that you created the projects in. The templates keep changing between versions, so it is a lot of work to finish a book in a different version. And get your iPhoto Books printed before March 31., Some forum members have posted here, that Apple employees at the the Apple Stores told them that printing books from iPhoto will no longer be possible after March 31. iPhoto 9.6.1 is working on El Capitan, but the support for iPhoto is no longer guaranteed.