Can the parent include words the child says imitatively?

No, the LDS is intended to reflect the child’s spontaneous vocabulary, not words the child understands or can say only in imitation.  However, parents should include words the child mispronounces or says in baby talk (such as “blankie” for “blanket”) or words that have a somewhat different meaning than is customary in adult usage (e.g., the child says “doggie” to include wolves as well as dogs).