In a real fair competition, LH would not just have a really hard time against EK&Co, but they would wipe the floor with LH.
Only German & other states extreme protectionism is keeping LH and it's less-than-ideal management afloat. If the ME3 get proper 5th freedom (something that LH has in DXB, for example, with LX offering DXB-MCT) in Germany and Europe as a whole (not just the few MXP flights) then it would be truly fair. Right now, the ME3 are fighting with shorter swords yet have the advantage. Give them the same tools, and the likes of LH and AF will get crushed (won't hurt for their arrogant pilots and management..)