Pronoun Agreement with Compound Antecedents

Usually, a pronoun refers to an individual noun, which is called the pronoun’s antecedent. Sometimes, however, a pronoun has more than one antecedent.

In the following sentence, for example, the pronoun they refers to John and to his brother:

John and Elaine enjoyed their trip.

When two or more antecedents are joined by and, the pronoun that refers to them should be plural, as in the example.

However, when two or more antecedents are joined by or, the pronoun refers to only one of the antecedents. In that case, the pronoun should agree with the nearer antecedent, as in the following examples:

Neither Ted nor his brothers found their keys.
Neither his brothers nor Ted found his keys.

In which sentence does the pronoun correctly agree with its antecedent? Karen or Lisa will deliver her report next. Karen or Lisa will deliver their report next.