Allport used to conduct research on personality.

the lexical approach

Explanation:

Gordon Allport was a respected and influential American scholar who worked in the field of psychology. Allport, son of a medical father and a teaching mother, was the youngest of four brothers. This translated into a keen interest in understanding human motivation, impulses and personality, which led him to develop the theory of personality traits. To conduct personality research, Allport used to use a lexical approach to reach his conclusions.

there are no options provided but you can choose among the following gender-neutral pronouns: zir, hir, eir, vis, tem, eir.

in the normal course of maintaining a pronoun-antecedent agreement, we could have used the words his or her but since we are also required to use gender-neutral language, we need to replace it with its equivalent gender-neutral pronoun.