The correct answer is Before the lecture, they will hand out packets of information.
Explanation:
In sentences, it is common a noun previously mentioned is replaced later using a pronoun such as she, he, they, etc.; this makes the sentence to flow naturally as it avoids repetition of the same noun. For example, in the sentence "Gabriella does not like vanilla ice cream; she prefers chocolate one" the noun Gabriella is later replaced by the pronoun "she". Also, Gabriella is considered as the antecedent.
This does not occur in the sentence "Before the lecture, they will hand out packets of information" because there is not an antecedent for the pronoun "they" or there is not mentioned who or what will hand out the packets of information.
