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Say my opponent has 2 life left and I have 0 cards left in my library. I cast Electrolyze doing two damage to opponent. It resolves.
Does he die before I deck myself, or do we simultaneously lose? That is, does the wording on Electrolyze mean "Electrolyze deals 2 damage divided as you choose among one or two targets and then you draw a card", or do both effects occur simultaneously?
It's a draw.
While the 'lethal' effects do not occur simultaneously, the state-based actions that check whether a player loses only happen after the spell resolves, not during its resolution:
608.2. If the object that's resolving is an instant spell, a sorcery spell, or an ability, its resolution may involve several steps.
116.3b The active player receives priority after a spell or ability (other than a mana ability) resolves.
704.3. Whenever a player would get priority (see rule 116, "Timing and Priority"), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event.
After Electrolyze resolve, state-based actions are checked:
104.3b If a player's life total is 0 or less, that player loses the game the next time a player would receive priority. (This is a state-based action. See rule 704.)
104.3c If a player is required to draw more cards than are left in their library, they draw the remaining cards and then lose the game the next time a player would receive priority. (This is a state-based action. See rule 704.)
104.4a If all the players remaining in a game lose simultaneously, the game is a draw.
