When I first began I thought that if there was no pop-up for instances of inbreeding, the lion simply was clean. Later, I learned this wasn't true, and I constantly have to ask chat to double check for me haha (you're a lifesaver chat!)
I think it would be really helpful to have the popup for all of the lion's generations, so countless players wouldn't get confused about their own lions, which while it doesn't affect anything ingame, it affects trades, worth of the lion, and takes a lot of time!