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The reason why the lead was transported from the Spanish mainland to the Balearic Islands, even though silver mines were in operation on the islands, has not been established.

Allow me to speculate:

Sailing ships need ballast in the keel to keep from capsizing when the wind blows on their sails. Normally this ballast is taken out of the ship only when it is beached for repairs or recaulking if it's seams.

When the Spanish returned from the New World with gold and silver, they removed the ballast from their keels and replaced it with gold and silver, thus allowing the maximum cargo for the voyage home.

My theory is that ships were sailing to the Balearic Islands with lead ballast, removing it, and returning to the mainland with silver ballast (as cargo.) Usually, rock was used as ballast, but if you have to remove it and replace it on a regular basis, it might have been faster to physically remove a smaller volume of lead than it is a larger volume of equal weight rock.