“Everyone else's life” vs “... else's lives”
Solution 1:
Everyone else's life would be correct. In this case everyone is a singular pronoun. (See this explanation of everyone being singular.) Else is just a determiner used after everyone.
Allow me a digression that I think you might find helpful when thinking about whether to use life or lives in similar sorts of construction. The most memorable explanation of whether to use a plural or singular word that I've ever encountered comes from the book Words Into Type (p. 357). Under the heading and subheadings of Nouns, Number, Singular with a plural possessive there is this clear explanation:
To avoid ambiguity a singular noun is often used with a plural possessive when only one of the things possessed could belong to each individual.
Manufacturing helps many people in the smaller cities to earn their living.
Forbes knew most of them by their first name.
Some of them could not pay their rent.
They eyed each other furtively and cursed beneath their breath.
Similarly:
Think of the last name of five pupils in the room.
The steam line ruptured, causing the death of seven longshoremen.
They doubled their efforts to discover the identity of two men who struck a man with their automobile and then fled.
Care must be taken not to apply the rule to the wrong noun.
Wrong: It is pretty clear that the smile on the face of the delegates, whenever they look at each other, is not a sincere one.
Right: ...on the faces of the delegates ... [ Smile is the noun the rule applies to.]