Only the “outties” version (the former one, if I understood you correctly) is necessary. The other one is an internal shoulder rotation exercise (“innie”) which shouldn’t be included in training.

I think Scooby once showed something similar to that one with DB.
He laid on his side and did these lateral once and then laid on his other side and lifted them from the floor (anteriorly)

are both good or only the lateral one?

Here is an example of reverse L-fly:

http://www.youtube.com/watch?v=HjDR4bOq9Mk

This channel shows many other variations with pulleys (although they don’t use full ROM, the proper way would be to rotate the humerus all the way, like the guy in the first video does):

http://www.youtube.com/watch?v=oRV57hXCsWs

I’m not sure what is the Reverse-L-Fly.
I tried looking for it but the more videos I see the more variations and different exercises appear on the screen. Some are not even related to others at all!

Will it be possible for you to post a link to a video here?

Heah kokia, it sounds like the shoulder had too much stress. Rest it and please see a doctor, because if the pain hasn’t gone away after more than half a week, you need to have this looked at.

All the best and get well!