Q:
Lionguard Longsword -- Karma, Craft, or Dungeon?
A:
I assume it’s from the cultural weapon vendors in lions arch.
Near the south area in LA (by the WvWvW/Heart of the mists portals) and right above the bar with the moose head there are 3 cultural weapon vendors. I assume they have the lionguard weapons.
Also, the info on the sword is:
http://www.gw2db.com/items/54562-lionguard-longsword
Zenyatoo is right. I have just bought a weapon there for skin. it costs Karma.