Okay, I know this is wrong (now). And I know the song is Caribbean Queen - but when sung there are not enough syllables in it.
Regardless of what I thought once, it still sounds better as Caribou Queen...
I think of a woman, Lady Godiva like, riding a Caribou and the singer desperate for a relationship with the beautiful and exotic woman - Queen of the Caribous.
She lives free and wild in the north, and he has that same dream, hence "living the same dream".
Despite never meeting her, he knows they are destined, "Our hearts they beat as one".
And, he know he came tame her, together in the lake of the midnight sun, "no more love on the run".
And that is just how that man, a tiger himself, was tamed.