While not on the stack, the characteristics of a split card are the combination of its two halves. For example, Destined|Lead is a green and black card, it is both an instant card and a sorcery card, and its converted mana cost is 6. - 4/18/2017
If I exile Reason // Believe with Living Lore's triggered ability, will he enter the battlefield as a 6/6?
Yes; the mana cost of Reason to Believe, a split card, "is the combined mana costs of its two halves" (C.R. 708.4b), and its converted mana cost is based on that mana cost, so is 6 (C.R. 202.3). Thus, Living Lore's power and toughness would be 6/6 since Reason to Believe's converted mana cost is 6.
If I exile Reason // Believe with Living Lore's triggered ability, will he enter the battlefield as a 6/6?