Yes. Lorewise this is completely correct. Even if it is a bug, it should stay in, like Ava+Toss combo.

Lion demon finger is actually different entity than lion himself. so no matter which side is dead, as long as it IS a hero and sourced from that hand it got more powerful.    
working as intended ofc

Screwing around in demo mode, I found that if Lion dies from a reflected Finger he gets the bonus damage stack. Works with lotus orb and AM counterspell. Also if both lion and his target die he gets 2 stacks. Working as intended? my guess is no.

TIL Lion gets stacks from reflected fingers