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Can you equip "lionheart Executioner"?

Sure.
Implying that solution is to everyone who want battleground wins should transfer to horde. That will do the trick.
Or should log some opposite faction chars and leave them afk at spawn, that...

Battleground wins?
I hope You do know that there is huge imbalance between Horde and Alliance in battlegrounds, and horde wins 90%, and not by struggle, but crushing and graveyard/spawn ganking?