Not sure order: upgrade iPhoto and OS Mavericks?

So, I'm trying to figure out this order b/c I'm going in circles. I know I need to upgrade iPhoto from iphoto 11 9.3 to 9.5 before the library will work in Mavericks. BUT when I go to upgrade iPhoto, it says I have to have OS 9 or higher. I'm still on OS X 10.7.5 Lion - have option to update directly to Mavericks BUT I thought then mess up the iPhoto library?

Can you please help me get from here to there?

My Time Machine is updated to the minute, so I'm backed up. Is that sufficient or would you recommend something else?

Thanks!