Use the objective pronoun him over the subjective he in the phrase let him who, such as in the famous Biblical line, Let him who is without sin cast the first stone. The subject of the sentence is the speaker’s audience (or whoever is doing the letting), not the owner of the pronoun, thus the pronoun must take the objective form. To simplify the grammatical logic, remove the specifying phrase (who is without sin in the above example) and read only the main clause (Let him cast the first stone), which would make little sense with a subjective pronoun.
The same holds with the feminine: Prefer let her who to let she who.