You need to get the two fish away from each other, or follow some of the advice given above. If everything is left the same, the fish WILL fight again. I completely understand that you want your favorite fish together, but sometimes with some fish it just can't happen. You can try to put them together in the future but I really wouldn't try it until your lapradei is healed. The endli might pick on it even further because the lap is in a weaker state. Bichirs are a bit pricier than your average guppy so I wouldn't gamble on keeping them together just yet 
As for your questions about why the endli gets along with the ornate, some fish are just cranky towards other fish. I've got an endli that attacks any lower jaw I've put it with, but it's fine with any of the upper jaw species. (Which SUCkS cauz I love my endlis and I want them all together but oh well...)
Good luck with whatever you decide to do... but make sure you do it soon.
As for your questions about why the endli gets along with the ornate, some fish are just cranky towards other fish. I've got an endli that attacks any lower jaw I've put it with, but it's fine with any of the upper jaw species. (Which SUCkS cauz I love my endlis and I want them all together but oh well...)
Good luck with whatever you decide to do... but make sure you do it soon.