How to install screen door on outside?
I’d be careful screwing anything down through the threshold. 

The “lip” (ridge as you call it) is for keeping wind blown rain from backing up to your interior swinging door. 

An exterior swinging screen door would be difficult at best. You’ll need a screen door frame that is “L” shaped that will lap over the existing door frame. I doubt if you’ll find one that is the exact correct depth, so you’ll need to install furring stripes on the head and jambs. Sealing the head is usually with flashing, but maybe you could use glazing tape. 

Likewise for sliding screen doors you’ll have similar installation problems. 

My daughter just installed magnetic screens on her deck door and she (and her dogs) love it.