Can someone explain how the dice rooms work?
http://bindingofisaacrebirth.gamepedia.com/Rooms#Dice_Rooms
1 and 6 will reroll your character's items. Those are the most important.
I would personally guess thatThe Lamb is supposed to be a fully-corrupted version of Isaac, similar to how you fight Isaac and Blue Baby on the other endgame route.
That was my first thought. Most (if not all) of the characters seem to be Isaac's interpretations of himself after reading the bible, so I'd tend to agree.