If I steal an opponent's B.F. Sword using Akshan's ability, and use Lucian's Weapon Master ability to equip it to Lucian, and my Akshan dies, what happens to the B.F. Sword?

When your Akshan leaves the board, the control-change effect granted by his ability ceases to apply. Here is what happens to the B.F. Sword:

1. Control Returns: Because the effect that gave you control of the equipment is no longer active, control of the B.F. Sword reverts to its original owner.
2. Attachment Remains: The equipment does not automatically detach or return to the owner's hand or base simply because control changed. It remains attached to Lucian.
3. Opponent's Options: Now that your opponent is the controller of the B.F. Sword again, they can use their own abilities (such as their own Weaponmaster effects or Equip abilities) to move the equipment to one of their units. Until they do so, it remains attached to your Lucian, but you no longer control it and cannot use its abilities.

This is supported by RiftJudge FAQ #694, which clarifies that stolen equipment remains on the new unit even after the Akshan that stole it leaves play, and that control returns to the original owner at that time.