I support this!
Funny thing is, I was thinking of the same thing the other day. I was playing The Simpsons: Tapped Out game and when something finishes on there it sends a notification to your phone to let you know it's done and I thought, 'It would be cool if LioDen could do something like that'.

I often forget when I put lionesses out to hunt or subs on patrol so it would be neat if you got notifications when they finished. I hope they do think about your idea, I love it :)

Same, I often switch between my phone and my kindle (both Amazon products) and I have lots of other apps on both so I get easily distracted so it'd be nice for that gentle reminder to be there :)

Also, if they were to take this suggestion under consideration, you might want to put in the main post about it being available on the Amazon Appstore as I've noticed that it quite often gets left out for most apps :(