If I wanted to say “I told her”, does it make sense to say j’ai la dit. I know when you translate it it usually says je lui ai dit.
You can't use that syntax.
You can't put a pronoun in the middle of a conjugated verb, only adverbs like pas (Je ne lui ai pas dit). The pronoun needs to be before the verb.
La is a direct object pronoun, but her (elle) is an indirect object of dire (j'ai dit à elle) so the right pronoun is lui, regardless of the gender. Lui means both to him and to her.
je lui ai dit.
Should you have used a direct object, la would have been the right pronoun:
La vérité, je l'ai dite.
or even both a direct and indirect object:
Ma sœur, la vérité, je la lui ai dite.